Authors:Salim Lahmiri; Stelios Bekiros Pages: 1 - 5 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Salim Lahmiri, Stelios Bekiros A rolling-window based approach is adopted in the current work to gauge time evolution of long-range dependence in a large set of various alternative (nonconventional) markets including Islamic, sustainability, ecology, and ethical equity markets. The approach allows conveying important information about the dynamics of long-range dependence in such contemporary and trendy alternative investments. The study shows that all investigated “alternative” markets exhibit persistence/anti-persistence dynamics, except two which reveal pure random behaviour. Roughly half of the Islamic markets and all ecological markets demonstrate persistent dynamic behaviour. On the contrary, all sustainable and most of the ethical alternative markets show increased anti-persistence. The persistence/anti-persistence patterns observed are cyclical, namely they are clustered over time. Finally, the distributions of estimated Hurst exponents are statistically different within Islamic and non-Islamic alternative markets.

Authors:Romanic Kengne; Robert Tchitnga; Sandrine Mabekou; Blaise Raoul Wafo Tekam; Guy Blondeau Soh; Anaclet Fomethe Pages: 6 - 17 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Romanic Kengne, Robert Tchitnga, Sandrine Mabekou, Blaise Raoul Wafo Tekam, Guy Blondeau Soh, Anaclet Fomethe The relay coupling of three fractional-order two-stage oscillators in the presence of time delay has been explored theoretically, numerically and analogically. The global stabilization of the system in a finite time is proven through Hölder and Gronwall inequalities, as well as through inequality scaling skills. The Synchronization of the system is characterized in terms of its parameters (coupling strength and time delay) by using time series, two parameters phase diagrams and two parameters transverse Lyapunov exponent diagrams. It is found that for smaller delay values, the network exhibits global phase synchronization whereas for higher delay values, phase synchronization just occurs between the two indirectly connected units (cluster phase synchronization). Striking phenomena such as amplitudes’ death and chaotic beats oscillations are also observed from this relay coupling of three fractional-order two-stage oscillators. Furthermore, PSpice simulation results of the analog electronic circuit are in perfect accordance with both theoretical and numerical results.

Authors:Feng Liang; Valery G. Romanovski; Daoxiang Zhang Pages: 18 - 34 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Feng Liang, Valery G. Romanovski, Daoxiang Zhang We study Poincaré bifurcation for a planar piecewise near-Hamiltonian system with two regions separated by a non-regular separation line, which is formed by two rays starting at the origin and such that the angle between them is α ∈ (0, π). The unperturbed system is a piecewise linear system having a periodic annulus between the origin and a homoclinic loop around the origin for all α ∈ (0, π). We give an estimation of the maximal number of the limit cycles which bifurcate from the periodic annulus mentioned above under n-th degree polynomial perturbations. Compared with the results in [13], where a planar piecewise linear Hamiltonian system with a straight separation line was perturbed by n-th degree polynomials, one more limit cycle is found. Moreover, based on our Lemma 2.5 we improve the upper bounds on the maximal number of zeros of the first order Melnikov functions derived in [19].

Authors:Ahmad Naimzada; Marina Pireddu Pages: 35 - 43 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Ahmad Naimzada, Marina Pireddu We propose an exchange economy evolutionary model with discrete time, in which there are two groups of agents characterized by different structures of preferences. The share updating mechanism depends in a monotone manner on the goods’ consumption, described in terms of the calorie intakes. In such framework we investigate the existence of equilibria, their stability and the occurrence of multistability phenomena via a qualitative bifurcation analysis, which also highlights the presence of transcritical bifurcations.

Authors:Olcay Akman; Timothy Comar; Miranda Henderson Pages: 44 - 54 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Olcay Akman, Timothy Comar, Miranda Henderson Integrated pest management (IPM) utilizes a combination of control methods in order to control pest populations in agricultural systems. Here, we construct a stage structured impulsive integrated pest management with added prey refuge. By considering the ability of pests to hide from management strategies, we establish properties for pest eradication and permanence of the proposed system. Simulations of eradicated and permanent solutions are also included in order to illustrate the behavior of pest and predator populations.

Authors:T.F. Xu; W.L. Li; Zai-Dong Li; C. Zhang Pages: 62 - 67 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): T.F. Xu, W.L. Li, Zai-Dong Li, C. Zhang We investigate the dynamics of dark-bright vector soliton solutions in a spin-orbit coupled Bose–Einstein condensate with repulsive interaction by the imaginary time evolution. The phase diagram is obtained numerically in spin-orbit coupled Bose–Einstein condensate. We find that the spin-orbit coupling favors miscibility, and the energy detuning between the Raman beam and atom dominates the separation phase of the Bose gases. We also find that the spin-orbit coupled strength affects interaction types (attractive or repulsive) between the two dark-bright solitons.

Authors:Xiao-Jun Yin; Lian-Gui Yang; Quan-Sheng Liu; Jin-Mei Su; Guo-rong Wu Pages: 68 - 74 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Xiao-Jun Yin, Lian-Gui Yang, Quan-Sheng Liu, Jin-Mei Su, Guo-rong Wu In this article, the behavior of the equatorial envelope Rossby solitary waves with complete Coriolis force and the external source are investigated analytically. By the asymptotic method of multiple scales and perturbation expansions, a new cubic nonlinear Schrödinger equation with complete Coriolis force and the external source is derived to describe the evolution of equatorial envelope Rossby solitary waves. The equation is different from the common Schrödinger equation, it is more suitable for describing envelope Rossby solitary waves when the horizontal component Coriolis force is stronger near the equator. Using the equation, the features of generalized beta, the horizontal component of Coriolis force and the external source are presented. And then various periodic structures for equatorial envelope Rossby solitary waves are obtained with the help of Jacobi elliptic functions and elliptic equation. Particularly, the solution of envelope Rossby solitary waves is obtained and graphical presentations are shown for Rossby solitary waves amplitude with the different Coriolis parameters. It is pointed out that with decreasing of Coriolis parameter λ, the amplitude of Rossby solitary waves decreases, whereas the propagating frequency is unchanged. And we find that the periodic solution of the nonlinear Schrödinger equation have different structures with a phase-locked diabatic heating source and without a source.

Authors:Yuu Miino; Tetsushi Ueta; Hiroshi Kawakami Pages: 75 - 85 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Yuu Miino, Tetsushi Ueta, Hiroshi Kawakami The Duffing equation describes a periodically forced oscillator model with a nonlinear elasticity. In its circuitry, a saturable-iron core often exhibits a hysteresis, however, a few studies about the Duffing equation has discussed the effects of the hysteresis because of difficulties in their mathematical treatment. In this paper, we investigate a forced planer system obtained by replacing a cubic term in the Duffing equation with a hysteresis function. For simplicity, we approximate the hysteresis to a piecewise linear function. Since the solutions are expressed by combinations of some dynamical systems and switching conditions, a finite-state machine is derived from the hybrid system approach, and then bifurcation theory can be applied to it. We topologically classify periodic solutions and compute local and grazing bifurcation sets accurately. In comparison with the Duffing equation, we discuss the effects caused by the hysteresis, such as the devil’s staircase in resonant solutions.

Authors:Gamal M. Mahmoud; Emad E. Mahmoud; Ayman A. Arafa Pages: 86 - 95 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Gamal M. Mahmoud, Emad E. Mahmoud, Ayman A. Arafa This paper deals with a kind of synchronization of dynamical systems with complex variables which is called generalized complex modified hybrid function projective synchronization (GCMHFPS) of time delay complex chaotic (hyperchaotic) systems. In other words, that the time delay complex systems can be synchronized up to a complex function transformation matrix. Moreover, the elements of the transformation matrix are complex functions of the states of drive system and time, where this matrix is not square. The idea of an active control method based on complex Krasovskii–Lyapunov functional is used to achieve GCMHFPS of time delay complex systems. Furthermore, based on the non-diagonal complex function transformation matrix, the modules and phases errors between one state of the complex response system and more than one of the states of the drive system are studied which have not been discussed before as far as we know. The analytical expression regarding the stability of this technique is derived and excellent agreement is found upon comparison with numerical calculations. In particular, we show through studying the time evolution of error, modulus and phase that the proposed scheme is effective for controlling time delay complex systems.

Authors:Yao Liu; Yashun Wang; Xun Chen; Huangchao Yu Pages: 96 - 107 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Yao Liu, Yashun Wang, Xun Chen, Huangchao Yu Spherical conformal contact is widely used in engineering structures. The existing solution of the spherical conformal contact problem always ignores the microscopic characteristics or friction of the spherical surfaces. Therefore, the current paper presents a spherical fractal model to characterize the contact state of spherical pairs considering the microscopic topography of rough spherical surface and the factor of friction. Firstly, a method of characterizing the microscopic topography of rough spherical surface is proposed based on three-dimensional Weierstrass–Mandelbrot function. The fractal contact model of the single asperity is developed by Hertz theory in combination with elasticity. Then, the macroscopic parameters are introduced to construct the contact surface coefficient. The area distribution function under conformal contact region is obtained. Considering the friction factor of the conformal contact region, the microcontact model of the spherical conformal contact is developed based on fractal theory. Finally, the formula between (elastic, elastic-plastic, plastic) contact area, (elastic, elastic-plastic, plastic) contact load and the key parameters (fractal parameters and macro parameters) are derived based on the proposed model. The relationship between the actual contact area and the normal load of the contact region is established. Numerical results show that the proposed model is more accurate for the analysis of the spherical surface contact area and contact load.

Authors:Fahimeh Nazarimehr; Karthikeyan Rajagopal; Jacques Kengne; Sajad Jafari; Viet-Thanh Pham Pages: 108 - 118 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Fahimeh Nazarimehr, Karthikeyan Rajagopal, Jacques Kengne, Sajad Jafari, Viet-Thanh Pham In this paper, a new multi-character dynamical system is proposed. It has chaotic and hyper-chaotic attractors without any equilibrium, with a line of equilibria or with unstable equilibrium. It means that the proposed system can change its characteristic by varying its parameters. This system shows multi-stability between different attractors such as quasi-periodic and chaotic attractors, quasi-periodic and periodic attractors, two periodic attractors and also two chaotic attractors.

Authors:Kolade M. Owolabi; Abdon Atangana Pages: 119 - 127 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Kolade M. Owolabi, Abdon Atangana In this paper, we develop a range of efficient and fast fractional difference schemes for the approximation of Caputo time-fractional subdiffusion-reaction equations. The classical time derivative is replaced with the Caputo fractional derivative operator. The experimental results justify that the numerical solution of the proposed methods compares favourably with the exact solution. Experimental results give a clear indication that dynamical models with non-integer order can yield a better spatial pattern when compared with their classical counterparts.

Authors:J.E. García-Farieta; R.A. Casas-Miranda Pages: 128 - 137 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): J.E. García-Farieta, R.A. Casas-Miranda Cosmological observations reveal that the Universe has a hierarchy of galaxy clustering with a transition to homogeneity on large scales according to the ΛCDM model. On the other hand some observational estimates suggest a multifractal behavior where galactic clustering is based on generalization of the correlation dimension. From this point of view, we study the influence of veto areas on fractal measurements in masks of galaxy surveys. Particularly we investigate if these holes can produce fractal behaviors or modify the scale of cosmic homogeneity. From the footprint of the Baryon Oscillation Spectroscopic Survey (BOSS) data release (DR12), we build a homogeneous sample following the radial selection function for 73,412 points limited to the redshift range 0.002 < z < 0.2. Different percentages of observational holes were created cumulatively in right ascension and declination on the sample. For the synthetic sample and for a real sample of galaxies we determined the fractal dimension Dq (r) in the range 2 ≤ q ≤ 6 using the sliding window technique to characterize the spatial point distribution. Our results show that generalized dimension varies with the scale, for low scales there are a fractal behavior with fluctuations for all hole percentages studied and for larger scales than 113 Mpc/h the statistical homogeneity is achieved in concordance with other analysis. We find that observational holes cause a shift in the homogeneity scale rH , in particular for all synthetic samples with percentages of holes between 0 and 10% the homogeneity scale is reached at (83 ± 1) Mpc/h while the fractal dimension changes as 2.83 ± 0.09 ≤ Dq ≤ 2.855 ± 0.09. For synthetic samples with percentages of holes greater than 10%, we find that the value of rH increases proportionally. Consequently future results about homogeneity scale based in fractal analyses must be corrected by observational holes and regions of incompleteness in the geometry of the galaxy catalogue if the size of the veto mask is significant.

Authors:Daisuke Ito; Hiroyuki Asahara; Takuji Kousaka; Tetsushi Ueta Pages: 138 - 145 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Daisuke Ito, Hiroyuki Asahara, Takuji Kousaka, Tetsushi Ueta DC–DC switching converters which are frequently treated as hybrid dynamical systems exhibit complex behavior due to nonlinear and interrupt characteristics. For synchronous buck-converters, we propose a method to control chaotic behavior by pulse–frequency modulation. An input voltage, a duty ratio of PWMs, and so on, affect to the regulation characteristics of converters directly, but a frequency of PWMs is determined by the frequency characteristics of the converter and is set as a fixed value. The proposed chaos-control method suppresses chaotic responses by slightly perturbing the pulse frequency alone, therefore our method can stabilize unstable periodic orbits without influence on the voltage regulation scheme. To simplify the feedback controller, the condition of dimension reduction for the controlling gain vector is derived. The proposed controller achieves the stabilization without a current sensor. Numerical simulation and circuit implementation demonstrate the validity of this method.

Authors:Nishant Juneja; Kulbhushan Agnihotri; Harpreet Kaur Pages: 146 - 156 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Nishant Juneja, Kulbhushan Agnihotri, Harpreet Kaur The present paper deals with an eco-epidemiological prey–predator model with delay. It is assumed that infection floats in predator species only. Both the susceptible and infected predator species are subjected to harvesting at different harvesting rates. Differential predation rates for susceptible and infected predators are considered. It is shown that the time delay can even destabilize the otherwise globally stable non-zero equilibrium state. It is observed that coexistence of all the three species is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and central manifold arguments, stability of bifurcating periodic orbits is determined. Numerical simulations have been carried out to justify the theoretical results obtained.

Authors:Zhong-Zhou Lan; Bo Gao; Ming-Jing Du Pages: 169 - 174 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Zhong-Zhou Lan, Bo Gao, Ming-Jing Du In this paper, we investigate a (2+1)-dimensional coupled nonlinear Schrödinger system, which describes the transverse effects in an optical fiber, time-independent copropagation and field of optical soliton. Bilinear forms, dark one- and two-soliton solutions are derived by virtue of the Hirota method. Propagation and interaction properties of the dark solitons are discussed: (i) Amplitudes and velocities of the dark solitons are affected by the values of the wave numbers μ, λ and θ. (ii) Head-on and overtaking interactions between the two parallel dark solitons are discussed, where the amplitudes of the dark solitons remain unchanged after each interaction, implying that the interactions are elastic. (iii) Stationary dark solitons are depicted in this paper. (iv) Through the asymptotic analysis, elastic interaction between the two solitons is discussed analytically.

Authors:Lin Shi; Huilan Yang; Xin Wang; Shouming Zhong; Wenqin Wang Pages: 180 - 185 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Lin Shi, Huilan Yang, Xin Wang, Shouming Zhong, Wenqin Wang In this paper, the problem concerning synchronization is investigated for complex networks with time delay and asymmetric coupling. By decomposing the asymmetric coupling matrix and employing Lyapunov functional method, sufficient conditions are obtained for synchronization. Finally, two examples are reported to illustrate the effectiveness of some proposed methods.

Authors:Jean-Marc Ginoux; Heikki Ruskeepää; Matjaž Perc; Roomila Naeck; Véronique Di Costanzo; Moez Bouchouicha; Farhat Fnaiech; Mounir Sayadi; Takoua Hamdi Pages: 198 - 205 Abstract: Publication date: June 2018 Source:Chaos, Solitons & Fractals, Volume 111 Author(s): Jean-Marc Ginoux, Heikki Ruskeepää, Matjaž Perc, Roomila Naeck, Véronique Di Costanzo, Moez Bouchouicha, Farhat Fnaiech, Mounir Sayadi, Takoua Hamdi A database of ten type 1 diabetes patients wearing a continuous glucose monitoring device has enabled to record their blood glucose continuous variations every minute all day long during fourteen consecutive days. These recordings represent, for each patient, a time series consisting of 1 value of glycaemia per minute during 24 h and 14 days, i.e., 20,160 data points. Thus, while using numerical methods, these time series have been anonymously analyzed. Nevertheless, because of the stochastic inputs induced by daily activities of any human being, it has not been possible to discriminate chaos from noise. So, we have decided to keep only the 14 nights of these ten patients. Then, the determination of the time delay and embedding dimension according to the delay coordinate embedding method has allowed us to estimate for each patient the correlation dimension and the maximal Lyapunov exponent. This has led us to show that type 1 diabetes could indeed be a chaotic phenomenon. Once this result has been confirmed by the determinism test, we have computed the Lyapunov time and found that the limit of predictability of this phenomenon is nearly equal to half the 90 min sleep-dream cycle. We hope that our results will prove to be useful to characterize and predict blood glucose variations.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Antonio Algaba, Cristóbal García, Manuel Reyes We solve, by using normal forms, the analytical integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system whose origin is an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x ˙ = x ( P 2 + P 3 ) , y ˙ = y ( Q 2 + Q 3 ) , with Pi, Qi homogeneous polynomials of degree i. We also prove that for any n ≥ 3, there are analytically integrable perturbations of x ˙ = x P n , y ˙ = y Q n which are not orbital equivalent to its first homogeneous component.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Jia He, Yumei Xue In this paper, we construct the evolving networks from hollow cube in fractal geometry by encoding. We set the unit cubes as nodes of network, where two nodes are neighbors if and only if their corresponding cubes have common surface. We also study some characteristics of the network, such as degree distribution, clustering coefficient and average path length. We obtain this network with small world and scale-free properties by the self-similar structure.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Jingshou Liu, Wenlong Ding, Junsheng Dai, Gang Zhao, Yaxiong Sun, Haimeng Yang Fractal theory has been widely applied in a variety of disciplines to understand the theory behind chaotic phenomena based on internal self-similarity. In this study, three ideal geological models are used to analyze the unreliability of the capacity dimension in the fractal calculation of geological bodies with different scales. Additionally, by varying the side length r of the statistical units, the geological meanings of the fractal dimension D and the correlation coefficient R2 are discussed. The points of information (POIs) are densely filled by binarizing the geological bodies to black/white. Based on the optimized r of a geological body, an algorithm is derived that divides the grids of the statistical units to determine the probability of the POIs falling into different grids. The information dimension (DI) and R2 of a geological body are obtained by fitting the variable data. An example calculation of the information dimension field in the Jinhu sag is presented to demonstrate the methodology and to test its reliability. The results show that determining the appropriate side length of the statistical unit is key to evaluating the fractal calculation. Compared to the capacity dimension, DI is more reliable in the fractal calculation of multi-scale geological bodies; DI is thereby the preferred fractal dimension to use in the analyses of these types of geological bodies.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Ghaus ur Rahman, Kamal Shah, Fazal Haq, Naveed Ahmad The present studies provide qualitative aspects of pine wilt disease model while incorporating convex incidence rate. Studying the nature of the proposed model, it is shown that the basic reproductive number completely determine various dynamics of the model. The global asymptotic stability analysis is expounded at different equilibrium points. The model has shown that the disease disappear, when the threshold quantity falls below unity. Numerical results are presented graphically to illustrate theoretical discussions.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): A. Jakubska-Busse, M.W. Janowicz, L. Ochnio, J.M.A. Ashbourn In this study Pickover biomorphs are analysed as being dependent on the chosen complex number system in which iterations of analytic functions are performed. Moran’s spatial autocorrelation function and two forms of entropy, the Shannon entropy and the sample entropy, are chosen in order to find correlations and measure complexity in Pickover biomorphs. These turn out to be strongly correlated and low-entropy objects with a fractal dimension between 1.4 and 2. It is shown that there is a strong maximum in correlation and a strong minimum in entropy for the case of Galilean complex numbers corresponding to the square of the generalised imaginary unit being equal to zero.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Francesca Grassetti, Cristiana Mammana, Elisabetta Michetti This work investigates the economic growth problem of establishing a relation between the elasticity of substitution between production factors, capital and output per-capita levels when dealing with a non constant elasticity of substitution production function. Starting from a discrete-time setup, some definitions of elasticity of substitution associated to an attractor are proposed and a general method to measure it is suggested. Thanks to this methodology a government may select a proper economic policy in order to reduce production costs without decreasing the capitalisation trend of the economy. The method proposed is applied to the Solow’s type growth model with differential savings using a Variable Elasticity of Substitution (VES) production function with constant returns to scale. It is found that when shareholders save more than workers or the elasticity of substitution is higher than one, a country characterised by production functions with higher elasticity of substitution experiences higher capital and output per-capita equilibrium levels. On the other hand, when the elasticity of substitution is lower than one and workers save more than shareholders, an ambiguous relation between elasticity of substitution and asymptotic dynamics is shown.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Liang Xu, Xianbin Cao, Wenbo Du, Yumeng Li Motivated by extensively applied tax policy in real society, we investigate the evolution of cooperation by incorporating tax mechanism into evolutionary game theory. We introduce two parameters: base tax rate p and progressive tax rate A. Players are taxed differentially depending on whether their payoffs exceed the average payoff of the system. Simulation results show that there is a non-monotonic influence in the fraction of cooperation as p increases for any given value of A; suitable p values are helpful to the existence of cooperators. We provide an explanation by studying the payoffs of players at the boundaries of cooperators. On the other hand, when we investigate the effect of A, we find that cooperation frequency increases monotonically with the increment of A for a relatively small value p, which is contrary to the effects when p is relatively large. To explain the nontrivial dependence of the cooperation level on A, we examine the number of players with high payoffs. In addition, we provide theoretical analysis of the cooperation level. Our work may be helpful in understanding the effect of tax phenomena on cooperative behavior.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): Adam Svenkeson, Bruce J. West We discuss how to generate an extended critical phase by controlling, with two control parameters, the transition rates of two-state stochastic units. The Langevin equation describing the mean field dynamics becomes strongly nonlinear and admits large fluctuations everywhere in the critical phase. Appropriate construction of transition rates allows the interacting system to be tuned to a critical line with the first control parameter, and then finely tuned along the critical line with respect to a tricritical point by adjusting the second control parameter. We introduce a basic model for interacting units, a perturbation of an existing opinion dynamics model, that displays these properties of extended criticality.

Abstract: Publication date: August 2018 Source:Chaos, Solitons & Fractals, Volume 113 Author(s): J.M. Munoz-Pacheco, E. Zambrano-Serrano, Ch. Volos, O.I. Tacha, I.N. Stouboulos, V.-T. Pham A novel fractional order dynamical system with a variable double-scroll attractor on a line, lattice and 3D grid is introduced. This system belongs to a class of chaotic systems with adjustable variables but with fractional order. Chaos generation only depends on the value of fractional order. As a result, a chaotic attractor is discovered and propagated in y-line. By introducing two extra control parameters, we also observed that the chaotic attractor varies in x-line, z-line, x − y -lattice, x − z -lattice, y − z -lattice, and 3D-grid. Dynamics of the new system are discovered by using phase portraits, bifurcation diagrams, Lyapunov spectrum, Kaplan–Yorke dimension, dissipative measure. Finally, the proposed fractional order system is designed with analog electronic circuits. Circuit results are in concordance with theoretical findings.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Xiaohui Dong, Ming Wang, Guang-Yan Zhong, Fengzao Yang, Weilong Duan, Jiang-Cheng Li, Kezhao Xiong, Chunhua Zeng In this paper, the stochastic kinetics in a time-delayed foraging colony system under non-Gaussian noise were investigated. Using delay Fokker–Planck approach, the stationary probability distribution (SPD), the normalized variance β 2, skewness β 3 and kurtosis β 4 of the state variable are obtained, respectively. The effects of the time delayed feedback and non-Gaussian noise on the SPD are analyzed theoretically. The numerical simulations about the SPD are obtained and in good agreement with the approximate theoretical results. Furthermore, the impacts of the time delayed feedback and non-Gaussian noise on the β 2, β 3 and β 4 are discussed, respectively. It is found that the curves in β 2, β 3 and β 4 exhibit an optimum strength of feedback where β 2, β 3 and β 4 have a maximum. This maximum indicates the large deviations in β 2, β 3 and β 4. From the above findings, it is easy for us to have a further understanding of the roles of the time delayed feedback and non-Gaussian noise in the foraging colonies system.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): B. Nana, S.B. Yamgoué, R. Tchitnga, P. Woafo We report the modeling for analysis of electrical clippers with side to side oscillating blade. The mathematical expressions for the study of its electromechanical dynamics are derived from the application of electromagnetics as well as mechanics laws. Numerical and analytical investigations reveal that, for well chosen range of its control parameters the efficiency of such clippers can be significantly improved, while the electrical power consumption is optimized. Chaotic behavior is investigated numerically using bifurcations diagrams. Experimental results match up well the theoretical predictions.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Payam Sadeghi Shabestari, Shirin Panahi, Boshra Hatef, Sajad Jafari, Julien C. Sprott For non-invasively investigating the interaction between insulin and glucose, mathematical modeling is very helpful. In this paper, we propose a new model for insulin-glucose regulatory system based on the well-known prey and predator models. The results of previous researches demonstrate that chaos is a common feature in complex biological systems. Our results are in accordance with previous studies and indicate that glucose-insulin regulatory system has various dynamics in different conditions. One interesting feature of this new model is having hidden attractor for some set of parameters. The result of this paper might be helpful for better understanding of regulatory system that contains glucose, insulin, and diseases such as diabetes, hypoglycemia, and hyperinsulinemia.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Pengfei Xu, Yanfei Jin This paper investigates the mean first-passage times (MFPTs) of a delayed tristable system driven by correlated multiplicative and additive noises. The results suggest that the correlation between the multiplicative and additive noises can induce symmetry-breaking in the delayed tristable system. The noise-induced dynamics, such as the noise enhanced stability (NES) and the resonant activation (RA), can be observed with considering the combined influences of correlated noises and intermediate stable state. The time delay plays an important role in the MFPTs. For example, with respect to the middle well, the increase of time delay results in the weakening of the stability of the two lateral wells; thus, all the MFPTs are decreased notably. Moreover, a law of MFPTs is established for three different potential wells. That is, the MFPT T(s 1 → s 3) (between the left and right wells) is equal to the sum of T(s 1 → s 2) (from left well to middle one) and T(s 2 → s 3) (from middle well to right one). However, this change regulation can be first broken with an increase in time delay, and then restored with the increase of correlation between noises.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Sajad Ali, Mushtaq Ahmad, M. Farooq In the present article coupled drift-ion acoustic mode is investigated in four component collisional, magnetized, and inhomogeneous ambiplasma consisting of positive and negative ions, non-thermal electrons and positrons. Linear dispersion relation for the coupled mode is derived with effect of nothermality and particle concentration. In the presence of weak dispersion and dissipation a KdV-Burger equation is derived in nonlinear regime, for coupled acoustic-drift shock and soliton. Using Tanh-method the solution for double layers in the system is derived. The results are numerically highlighted for ambi plasma at early universe and space plasma. Further more keeping in view the non thermal behavior of ambiplasma in space, a kappa distributed approach is used for these calculations.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Zhiying Chen, Yong Liu, Ping Zhou Fractal dimension is the most important parameter for surface characterization. In this paper, four methods used to estimate the fractal dimensions of surface profiles and their applications in machined surfaces are studied. These methods are first evaluated using surface profiles created by Weierstrass–Mandelbrot function from the three aspects of fitting accuracy, calculation accuracy and calculation stability, and then applied to the machined rough surfaces. By comparing the results of the four methods, it is found that none of the methods is particularly prominent in all of the three aspects. However, the three point sinuosity method is found to be relatively the most suitable and reliable method among the four tested methods for extracting fractal dimensions of both generated and measured rough surface profiles.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Márcia L.C. Peixoto, Erivelton G. Nepomuceno, Samir A.M. Martins, Márcio J. Lacerda It has been shown that natural interval extensions (NIE) can be used to calculate the largest positive Lyapunov exponent (LLE). However, the elaboration of NIE are not always possible for some dynamical systems, such as those modelled by simple equations or by Simulink-type blocks. In this paper, we use rounding mode of floating-point numbers to compute the LLE. We have exhibited how to produce two pseudo-orbits by means of different rounding modes; these pseudo-orbits are used to calculate the Lower Bound Error (LBE). The LLE is the slope of the line gotten from the logarithm of the LBE, which is estimated by means of a recursive least square algorithm (RLS). The main contribution of this paper is to develop a procedure to compute the LLE based on the LBE without using the NIE. Additionally, with the aid of RLS the number of required points has been decreased. Eight numerical examples are given to show the effectiveness of the proposed technique.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Cong Wang, Hongli Zhang, Wenhui Fan, Ping Ma Chaotic oscillation in a power system is considered the main cause of power blackouts in large-scale interconnected power grids. The chaotic oscillation mechanisms and the control methods for chaos oscillation of power systems need to be analyzed. This paper thus proposed an adaptive control method for chaotic power systems using finite-time stability theory and passivity-based control approach. The adaptive feedback controller is first constructed using the finite-time stability theory and the passive theory to make the chaotic power system equivalent to a closed-loop passive system. We then proved that the passive power system can stabilize the equilibrium points. We also extensively studied fourth-order power system. Results show that the controller based on the finite-time theory and the passivity-based control approach can effectively stabilize the chaotic behavior within finite time. The control strategy was also found to be robust to the different power system states.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Tong Luo, Ming Xu, Yunfeng Dong A two-dimensional hyperbolic Hamiltonian system can be linearly stabilized by a Hamiltonian structure-preserving controller. A linear symplectic transformation and the Lie series method can successfully normalize the expanded Hamiltonian function around a controlled stable equilibrium point, then the dynamics in the controlled center manifolds of which can be described by a Poincaré section. With the implement of the inverse transformation of the Lie series, the analytical results of the controlled manifolds can be obtained. Applying normalization and analytical calculation to planar solar sail three-body problem, we can get the normal form of the corresponding Hamiltonian function and trajectory around the chosen equilibrium point by analytical results. Finally, typical KAM theory is used to analyze the nonlinear stability of the controlled equilibrium point, and the stable region of the control gains are given by numerical calculation.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Mingyuan Zhang, Boyuan Liang, Sheng Wang, Matjaž Perc, Wenbo Du, Xianbin Cao The increase in economic exchange, brought about by globalization and leaps of progress in science and engineering, has led to a sharp increase in air traffic density. As a consequence, airspace has become increasingly crowded, and limitations in airspace capacity have become a major concern for the future development of air travel and transportation. In this paper, we adopt methods of network science to analyze flight conflicts in the Chinese air route network. We show that air conflicts are distributed heterogeneously along the waypoints of the Chinese air route network. In particular, the frequency of flight conflicts follows an exponential distribution. The time-space investigation of flight conflicts shows that they are concentrated at specific regions of the Chinese air route network and at specific time periods of the day. Our work offers fascinating insights into one of the world's largest and most busiest air route networks, and it helps us mitigate flight conflicts and improve air traffic safety.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Sizhong Zhou, Hongxia Liu, Tao Zhang Many problems on computer science, chemistry, physics and network theory are related to factors, factorizations and orthogonal factorizations in graphs. For example, the telephone network design problems can be converted into maximum matchings of graphs; perfect matchings or 1-factors in graphs correspond to Kekulé structures in chemistry; the file transfer problems in computer networks can be modelled as (0, f)-factorizations in graphs; the designs of Latin squares and Room squares are related to orthogonal factorizations in graphs; the orthogonal (g, f)-colorings of graphs are related to orthogonal (g, f)-factorizations of graphs. In this paper, the orthogonal factorizations in graphs are discussed and we show that every bipartite ( 0 , m f − ( m − 1 ) r ) -graph G has a (0, f)-factorization randomly r-orthogonal to n vertex disjoint mr-subgraphs of G in certain conditions.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): S. Ijaz, S. Nadeem The present research article is focused to analyze the blood mediated nanoparticle transportation through the atherosclerotic artery. The wall property on the atherosclerotic artery is also assumed to create resemblance with permeability characteristic of the arterial wall thickness. Heat transfer property of the catheter wall as well as the arterial wall is taken into account for the purpose to attenuate the stenotic lesions. To discuss the problem, mathematical model is developed through phase flow approach with hybrid nanofluid phenomena. Arterial pressure in the stenotic artery is also discussed through tapering impacts. Further, flow configurations of hemodynamics are evaluated to discuss the flow of blood through atherosclerotic artery. The outcomes obtained in this analysis are useful in biomedical related application. It is concluded from this mathematical problem through graphical results that the use of Cu–Al2O3/blood is more suitable to reduce the resistance to flow of the atherosclerotic artery when compared to the case of Cu-blood. Moreover, a wall properties impact depicts that hemodynamics of atherosclerotic artery increases.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Navid Vafamand, Shapour Khorshidi, Alireza Khayatian This paper proposes a novel hyperchaotic secure communication scheme for non-ideal communication channels. The proposed approach employs Takagi–Sugeno (TS) fuzzy model and linear matrix inequality (LMI) technique to design a controller which synchronizes the hyperchaotic transmitter and receiver systems. In the presented method, only few numbers of states are needed to be transformed which is consistent with the practical limitations of a non-ideal channel and highly secure communication. Therefore, a robust fuzzy observer is proposed to estimate the other states of the transmitter at the receiver side. Furthermore, since the channel is non-ideal, H ∞ performance criterion is employed to derive robust observer and controller against the external disturbance and noise. In order to make the proposed approach more applicable, the sufficient controller and observer design conditions are formulated in terms of linear matrix inequalities (LMIs) which can be solved by convex optimization techniques. In addition, to further remove the effect of the noise on the information recovery, a moving average filter is utilized. Finally, to show the effectiveness and advantages of the proposed approach, the hyperchaotic Lorenz system is considered and the signal is analyzed at the transmitter and receiver sides. Then, the results obtained show the superiority and effectiveness of the proposed method compared with those of the existing approaches.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Zhenxi Niu, Jiwei Xu, Dameng Dai, Tairan Liang, Deming Mao, Dawei Zhao In this paper, we explore the effects of rational conformity behavior on the evolution of cooperation in prisoner's dilemma. In general, we think individual updates strategy is based on the difference in income between himself and his neighbors. In real life, in order to avoid risks, they may be consistent with most individuals in the group, because they are not the worst. Therefore, we divide the players into two categories, one is traditional players and the other is rational conformists who update their strategies are based on the two factors: payoffs and the behavior of most individuals in their nearest neighbors. Through a large number of simulations, we find that, rational conformity behavior can promote cooperation in the prisoner's dilemma game, and the greater the proportion of rational players, the more obvious the promotion of cooperation. Our work may provide further insight in understanding the evolution of cooperation, players selectively follow others and make some adjustments according to the current environment to make their own situation better.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): F. Panichi, G. Turchetti We discuss the stability of a Hamiltonian system by comparing the standard Lyapunov error (LE) with the forward error (FE) due to a small random perturbation. We introduce also the reversibility error (RE) where the evolution is computed forward up to time t and backwards to t = 0 in presence of noise. This procedure has been investigated in the case of symplectic maps, but it turns out that the results are simpler in the case of a noisy flow, in the limit of zero noise amplitude. Indeed the stochastic processes defined by the displacement of the noisy orbit at time t for FE, or at time 0 for RE after the evolution up to time t, satisfy linear Langevin equations, are Gaussian processes, and the errors are just their root mean square deviations. All the errors are expressed in terms of the fundamental matrix L ( t ) of the tangent flow and can be evaluated numerically using a symplectic integrator. Letting eL (t) be the Lyapunov error and eR (t) be the reversibility error a very simple relation holds e R 2 ( t ) = ∫ 0 t e L 2 ( s ) d s . The integral relation is quite natural since the local errors due to a random perturbations accumulate during the evolution whereas for the Lyapunov case the error is introduced only at time zero and propagated. The plot of errors for initial conditions in a Poincaré section reflects the phase portrait, whereas in the action plane it allows to single out the resonance strips. We have applied the method to a 3D Hamiltonian model H = H 0 ( J ) + λ V ( Θ ) , where analytic estimates can be obtained for the single resonances from perturbation theory. This allows to inspect the double resonance structure where the single resonance strips intersect. We have also considered the Hénon–Heiles Hamiltonian to show numerically the equivalence of the errors apart from a shift of 1/2 in the power law exponent in the case of regular orbits. The reversibility error method (REM), previously introduced as the error due to round off in the symplectic integration, appears to be comparable with RE also for the models considered here.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Xingyu Han We explore the valuation and hedging strategies of a European vulnerable option with funding costs and collateralization for local volatility models. It is found that, in the absence of arbitrage opportunities, the option price must lie within a no-arbitrage band. The boundaries of no-arbitrage band are computed as solutions to backward stochastic differential equations (BSDEs in short) of replicating strategy and offsetting strategy. Under some conditions, we obtain the closed-form representations of the no-arbitrage band for local volatility models. In particular, the fully explicit expressions of the no-arbitrage band for Black–Scholes model and the constant elasticity of variance (CEV) model with time-dependent parameters are derived. Furthermore, we provide a strategy for the option holder by using the risky bond issued by the option writer to hedge the remaining potential losses. By virtue of numerical simulation, the impact of the default risk, funding costs and collateral can be observed visually.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Dongmei Huang, Wei Li, Guidong Yang, Meijuan He In this paper, the dynamical properties of a real-power vibration isolation system with delayed feedback control subjected to deterministic and stochastic excitations are considered. According to the free vibration analysis, it is found that a large number of limit cycles may be existed for certain time delay and feedback gain. Then, the relationship of amplitude and frequency is derived for the undamped system. For the system with harmonic excitation, multi-valued phenomena are observed due to the existence of the limit cycles. In this respect, with the change of time delay, in every period the response is similar to time delay island, and the number of islands is different under different excitation frequency. Additionally, for analyzing the complex dynamic properties, the vibration isolation system with Gauss white noise excitation is explored by the largest Lyapunov exponent and the stationary probability density. The symmetrical period-doubling bifurcation phenomenon is found and verified. Finally, by using Monte Carlo simulation, the stationary probability density is explored from original system. The change of time delays can induce the occurrence of stochastic bifurcation and the response from two peaks becomes triple peaks.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Juanhui Zheng, Baotong Cui In this paper, we address the problem of state estimation of the Lurie system via the communication channel in the case of only this system outputs available. A coder-decoder scheme combines with a logarithmic quantization to form a novel and reliable communication channel. The errors between Lurie system outputs and observer outputs are regarded as the feedback signals, which are transmitted into the observer though the communication channel. A sufficient condition for input-to-state stability is given for the boundedness of the error of state estimation. The results of two examples show the effectiveness and superiority of the proposed communication channel of the logarithmic quantization.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Haide Gou, Baolin Li This paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of properties of Hilfer fractional calculus, the theory of propagation family as well as the theory of the measure of noncompactness and the fixed point methods, we obtain the existence results of mild solutions for Sobolev type fractional evolution differential equations involving Hilfer fractional derivative. Finally, two examples are presented to illustrate the main result.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Mohammad Hossein Heydari, Zakieh Avazzadeh In this study, the Poisson equation is generalized with the concept of variable-order (V-O) fractional derivatives called variable-order fractional Poisson equation (V-OFPE). In order to find an accurate solution of this system, we establish an optimization method through the Legendre wavelets (LWs). To carry out the method, we firstly derive an operational matrix (OM) of V-O fractional derivative for the LWs to be employed in expanding the unknown solution. Then, the function of residual is applied to reform the V-OFPE to an optimization problem which leads to choose the unknown coefficients optimally. In the final step, we implement the constrained extremum method which adjoins the objective function implied from the two-norm of residual function and the constraints corresponded to the given boundary conditions by a set of Lagrange multipliers. Accordingly, the final optimal conditions are actually the algebraic equations including the expansion coefficients and Lagrange multipliers. Theoretical convergence and error analysis of the approximation procedure using the LWs are investigated. In addition, the applicability and computational efficiency are experimentally examined for some illustrative examples.

Abstract: Publication date: July 2018 Source:Chaos, Solitons & Fractals, Volume 112 Author(s): Sajad Jafari, Soroush Dehghan, Guanrong Chen, Sifeu Takougang Kingni, Karthikeyan Rajagopal This paper introduces a chaotic system in the spherical coordinates which, when expressed in the Cartesian coordinate system, has a chaotic attractor located in an impassable sphere like a bird in the cage. It also has a coexisting attractor outside that sphere. Basic dynamical properties of this system are investigated and its FPGA realization is demonstrated.