Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): Xiaodi Li, Feiqi Deng Although the well-known Razumikhin method has been well developed for the stability of functional differential equations with or without impulses and it is very useful in applications, so far there is almost no result of Razumikhin type on stability of impulsive functional differential equations of neutral type. The purpose of this paper is to close this gap and establish some Razumikhin-based stability results for impulsive functional differential equations of neutral type. A kind of auxiliary function N(t) that has great randomicity is introduced to Razumikhin condition. Some examples are given to show the effectiveness and advantages of the developed method.

Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): R.P. Sreejith, Jürgen Jost, Emil Saucan, Areejit Samal We have recently introduced Forman’s discretization of Ricci curvature to the realm of complex networks. Forman curvature is an edge-based measure whose mathematical definition elegantly encapsulates the weights of nodes and edges in a complex network. In this contribution, we perform a comparative analysis of Forman curvature with other edge-based measures such as edge betweenness, embeddedness and dispersion in diverse model and real networks. We find that Forman curvature in comparison to embeddedness or dispersion is a better indicator of the importance of an edge for the large-scale connectivity of complex networks. Based on the definition of the Forman curvature of edges, there are two natural ways to define the Forman curvature of nodes in a network. In this contribution, we also examine these two possible definitions of Forman curvature of nodes in diverse model and real networks. Based on our empirical analysis, we find that in practice the unnormalized definition of the Forman curvature of nodes with the choice of combinatorial node weights is a better indicator of the importance of nodes in complex networks.

Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): Husin Alatas, Salamet Nurhimawan, Fikri Asmat, Hendradi Hardhienata In this report we discuss a simple agent based model for opinion dynamics where each of agent have complete social connectivity network with other agents. The state of an agent is described by three attributes. In our model, both the opinion level and attributes of an agent are affected by its social connectivity with other connected agents. We also introduce the notions of opinion and connectivity perception indices to characterize the intrinsic behavior of an agent that influence its connectivity with the corresponding connected neighbors. Shannon-like entropy is used to describe the dynamical characteristics of the developed model in terms of opinion level. The opinion dynamics in the presence of isolated and stubborn agents are also discussed. We found that the presence of stubborn agents demonstrate a remarkable phase-transition phenomenon on the corresponding opinion levels.

Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): G.C. Das The main interest is to study the nonlinear acoustic waves in rotating plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation approximation causes the interaction of Coriolis force in the dynamics, and leads to the complexity in the derivation of the nonlinear wave phenomena. Pseudopotential method has been used to derive the Sagdeev-like wave equation with a view to exhibit the changes in solitary wave propagation. Some special methods have been developed to exhibit the salient features of the nonlinear waves which could be of interest in laboratory as well as in astroplasmas. As a result, findings of the compressive and rarefactive solitons along with the formation of shock waves, double layers, sinh-wave in rotating plasma ought to be of merit. Moreover, studies have expected exciting observations in generating the high energies which, in turns, yields the phenomena of soliton radiation and explosions or bursting of the solitary waves. Further, to support the theoretical investigations, some typical plasma parameters have been taken for the graphical presentation of the waves.

Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): Eunho Koo, Geonwoo Kim This paper concerns a catastrophe put option with default risk. Catastrophe events are described by the exponential jump model, and the default event of the option issuer is specified by the intensity based model with a stochastic intensity. Under this model, we derive the explicit analytical pricing formula of a catastrophe put option with default risk by using the multidimensional Girsanov theorem repeatedly. We also observe the effects of default risk on the prices of a catastrophe put option through the numerical experiment.

Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): Euaggelos E. Zotos The planar linear restricted four-body problem is used in order to determine the Newton–Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position as well as of the stability of the libration points is monitored when the values of the mass parameter b as well as of the angular velocity ω vary in predefined intervals. The regions on the configuration (x, y) plane occupied by the basins of attraction are revealed using the multivariate version of the Newton–Raphson iterative scheme. The correlations between the attracting domains of the equilibrium points and the corresponding number of iterations needed for obtaining the desired accuracy are also illustrated. We perform a thorough and systematic numerical investigation by demonstrating how the parameters b and ω influence the shape, the geometry and of course the fractality of the converging regions. Our numerical outcomes strongly indicate that these two parameters are indeed two of the most influential factors in this dynamical system.

Abstract: Publication date: August 2017 Source:Chaos, Solitons & Fractals, Volume 101 Author(s): Aavishkar Katti, R.A. Yadav We present a study of the one dimensional modulation instability due to a broad optical beam in pyroelectric photorefractive crystals where the space charge field is formed due to solely the pyrolectric effect. The one-dimensional growth rate of the modulation instability depends upon the intensity of the incident beam and the magnitude of the temperature change. Relevant example of a Strontium Barium Niobate crystal is taken to illustrate the theoretical analysis.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Marek Jaworski Evolution equations associated with the Schrödinger equation are derived for an arbitrary time-dependent potential. It is shown that the eigenvalues evolve according to the Hellmann–Feynman theorem, while the eigenfunction evolution can be determined either by solving a system of coupled differential equations or by a contour integration in the complex k-domain. A possible application to solving a class of Schrödinger spectral problems is also discussed.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Renxiang Shi, Jiang Yu We take the delays due to gestation of two kinds of zooplankton as parameters, the dynamics of a two zooplankton-phytoplankton model is studied, we discussed the dynamics under six conditions: (1) τ 1 = τ 2 = 0 , (2) τ 1 > 0 , τ 2 = 0 , (3) τ 1 = 0 , τ 2 > 0 , (4) τ 1 = τ 2 > 0 , (5) τ 1 ∈ (0, τ 10), τ 2 > 0, (6) τ 2 ∈ (0, τ 20), τ 1 > 0, the Hopf bifurcation about condition (5) should be studied by center manifold theorem and normal form. At last, some simulations are given to support our results

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): S.N. Raw, P. Mishra, R. Kumar, S. Thakur Defense mechanisms are very important to all animal life. Predators in every biome must eat to survive. With predators being top on the food chain and always on the lookout for a meal, prey must constantly avoid being eaten. In this paper, we have proposed and analyzed a tri-trophic predator–prey model of one prey and two predator exhibiting group defense mechanism. We have assumed Monod-Haldane functional response for interaction between species due to group defense ability of prey and middle predator. We have performed Kolmogorov and Hopf bifurcation analysis for the model system. Linear and global stability of the model system have been analyzed. Lyapunov exponents are computed numerically and 2D scan for different parameters of the model have performed to characterize the complex behavior of the model system. The numerical simulations shows the chaotic and periodic oscillations of the model system for certain range of parameter. We have drawn bifurcation diagrams for different parameter values which shows the complex dynamical behavior of model system. This work is an attempt to study the effect of group defense mechanism of prey in predator population and effect of immigration within top predator population is investigated. It is also observed that in the presence of group defense, the model system stabilizes after adding a small amount of constant immigration within top predator population.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): H. Vahed, Z. Salehnezhad Cavity solitons (CSs) have an important role as information bits in all optical information processing. In this paper, we switched on a new type of CS as excitable cavity soliton in the cavity soliton laser (CSL). Also, we compared the behavior of excitable CS with self-pulsing and stable CSs by using of suitable values for system parameters and then we designed logical gates (AND, OR) with excitable CSs in the CSL. The capabilities of excitable CSs has been studied to improve possibilities for designing of all optical gates.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): R. Alima, S. Morfu, P. Marquié, B. Bodo, B.Z. Essimbi In this paper, we analyze the conditions leading to the nonlinear supratransmission phenomenon in two different models: a modified fifth order Klein–Gordon system and a modified sine-Gordon system. The modified models considered here are those with mixed coupling, the pure linear coupling being associated with a nonlinear coupling. Especially, we numerically quantify the influence of the nonlinear coupling coefficient on the threshold amplitude which triggers the nonlinear supratransmission phenomenon. Our main result shows that, in both models, when the nonlinear coupling coefficient increases, the threshold amplitude triggering the nonlinear supratransmission phenomenon decreases.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Xian-Feng Li, Yan-Dong Chu, Andrew Y.T. Leung, Hui Zhang The paper presents a novel synchronization scheme for uncertain chaotic systems via complete-adaptive-impulsive controls. The controllers are designed in the form of linear-error feedback coupling, but the control gains are completely adaptive. More details on minimizing interaction terms and accelerating synchronization process are revealed. The interaction terms can be selected on the largest invariant set minimally, but would be optimized corroboratively to promote the stabilization. The analytic expressions of parameter update laws for identifying uncertain parameters are derived from a reasonable truncation directly. A representative chaotic system is employed to show that the present scheme is not only a tactful way of synchronizing chaotic systems with uncertainties imposed on nonlinear terms, but a more radical approach on achieving synchronization with relatively moderate control gains than existed methods.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Chengdai Huang, Yijie Meng, Jinde Cao, Ahmed Alsaedi, Fuad E. Alsaadi Recently, the dynamics of the fractional delayed neural networks has been considerably concerned. It is illustrated that time delay has a remarkable influence on the dynamical behaviors of the fractional neural networks. Nevertheless, the results of the fractional neural network with leakage delay are extremely few. It is the first time that the stability and bifurcation of fractional BAM neural networks with time delay in leakage terms is examined in the current paper. The stability criterion and the conditions of bifurcation are obtained for the proposed systems with or without leakage delay by selecting time delay as the bifurcation parameter. It is amazing that the leakage delay has a destabilizing influence on the stability performance of such system and they cannot be ignored. Moreover, the relation between the bifurcation point and the order is fully discussed by careful calculation. Finally, numerical examples are addressed to verify the feasibility of the obtained theoretical results.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Ali Bashan, Nuri Murat Yagmurlu, Yusuf Ucar, Alaattin Esen In this study, an effective differential quadrature method (DQM) which is based on modified cubic B-spline (MCB) has been implemented to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. After separating the Schrödinger equation into coupled real value differential equations,we have discretized using DQM and then obtained ordinary differential equation systems. For time integration, low storage strong stability-preserving Runge–Kutta method has been used. Numerical solutions of five different test problems have been obtained. The efficiency and accuracy of the method have been measured by calculating error norms L2 and Linfinity and two lowest invariants I1 and I2. Also relative changes of invariants are given. The newly obtained numerical results have been compared with the published numerical results and a comparison has shown that the MCB-DQM is an effective numerical scheme to solve the nonlinear Schrödinger equation.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Xiancheng Shi, Yucheng Feng, Jinsong Zeng, Kefu Chen An improved recursive Levenberg–Marquardt algorithm (RLM) is proposed to more efficiently train neural networks. The error criterion of the RLM algorithm was modified to reduce the impact of the forgetting factor on the convergence of the algorithm. The remedy to apply the matrix inversion lemma in the RLM algorithm was extended from one row to multiple rows to improve the success rate of the convergence; after that, the adjustment strategy was modified based on the extended remedy. Finally, the performance of this algorithm was tested on two chaotic systems. The results show improved convergence.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Arzu Akbulut, Filiz Taşcan In this work, we study Lie symmetry analysis for fractional order differential equations that is one of the applications of symmetries. This study deals with Lie symmetry of fractional order modified Korteweg–de Vries (mKdV) equation. We found Lie symmetries of this equation and then we reduced fractional order modified Korteweg–de Vries (mKdV) equation to fractional order ordinary differential equation with Erdelyi–Kober fractional differential operator. Then we used characteristic method for fractional order differential equations and help of founded these Lie symmetries for finding solutions for given equation. Then we obtained infinite and finite conservation laws of fractional order modified Korteweg–de Vries (mKdV) equation.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Xia Wang, Zihui Xu, Sanyi Tang, Robert A. Cheke Modeling external perturbations such as chemical control within each generation of discrete populations is challenging. Based on a method proposed in the literature, we have extended a discrete single species model with multiple instantaneous pesticide applications within each generation, and then discuss the existence and stability of the unique positive equilibrium. Further, the effects of the timing of pesticide applications and the instantaneous killing rate on the equilibrium were investigated in more detail and we obtained some interesting results, including a paradox and the cumulative effects of the incorrect use of pesticides on pest outbreaks. In order to show the occurrences of the paradox and of hormesis, several special models have been extended and studied. Further, the biological implications of the main results regarding successful pest control are discussed. All of the results obtained confirm that the cumulative effects of incorrect use of pesticides may result in more severe pest outbreaks and thus, in order to avoid a paradox in pest control, control strategies need to be designed with care, including decisions on the timing and number of pesticide applications in relation to the effectiveness of the pesticide being used.

Abstract: Publication date: July 2017 Source:Chaos, Solitons & Fractals, Volume 100 Author(s): Zhenghong Deng, Shengnan Wang, Zhiyang Gu, Juwei Xu, Qun Song Adopting the strategy of neighbor who performs better is crucial for the evolution of cooperation in evolutionary games, in that such an action may help you get higher benefit and even evolutionary advantages. Inspired by this idea, here we introduce a parameter α to control the selection of preferred opponents between the most successful neighbor and one random neighbor. For α equaling to zero, it turns to the traditional case of random selection, while positive α favors the player that has high popularity. Besides, considering heterogeneity as one important factor of cooperation promotion, in this work, the population is divided into two types. Players of type A, whose proportion is v, select opponent depending on the parameter α, while players of type B, whose proportion is 1 − v , select opponent randomly. Through numerous computing simulations, we find that popularity-driven heterogeneous preference selection can truly promote cooperation, which can be attributed to the leading role of cooperators with type A. These players can attract cooperators of type B forming compact clusters, and thus lead to a more beneficial situation for resisting the invasion of defectors.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Yongbao Liu, Qiang Wang, Huidong Xu The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of-freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincaré maps are established through choosing suitable Poincaré section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Ignacio S. Gomez By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the poles of the scattering matrix and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by characterizing the behavior of the Gamow model whose dissipative decay time, measured by its decoherence time, is found to be inversely proportional to the Lyapunov exponents of the unstable periodic orbits. The results are in agreement with those obtained by means of the semiclassical periodic–orbit approach in quantum resonances theory but using a simpler mathematics.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Daniel Olmos-Liceaga, Humberto Ocejo-Monge In this work we consider the periodic stimulation of two and three dimensional excitable media in the presence of obstacles with an emphasis on cardiac dynamics. We focus our attention in the understanding of the minimum size obstacles that allow generation of spiral and scroll waves, and describe different mechanisms that lead to the formation of such waves. The present study might be helpful in understanding and controlling the appearance of spiral and scroll waves in the medium.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Kolade M. Owolabi, Abdon Atangana This paper considers the Caputo–Fabrizio derivative in Riemann–Liouville sense for the spatial discretization fractional derivative. We formulate two notable exponential time differencing schemes based on the Adams–Bashforth and the Runge–Kutta methods to advance the fractional derivatives in time. Our approach is tested on a number of fractional parabolic differential equations that are of current and recurring interest, and which cover pitfalls and address points and queries that may naturally arise. The effectiveness and suitability of the proposed techniques are justified via numerical experiments in one and higher dimensions.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): J.D. Tchinang Tchameu, A.B. Togueu Motcheyo, C. Tchawoua We report numerical observations of scattering process of moving multibreathers by isolated impurities in the discrete nonlinear Schrödinger lattice representing the vibrational energy transport along the protein chain. It is found that, except for the multibreather passing, internal collision phenomenon support all types of scattering outcomes for both attractive and repulsive impurities. Furthermore, for large strength of attractive impurity the scattering of two-hump soliton can give rise to a trapping on a site other than the one containing the impurity. As concerns three-hump soliton, the passing, trapping and reflection are simultaneously carried out for some parameters. In the case of three-hump soliton introduced between two repulsive impurity sites, back and forth are observed as well as increasingly individualistic behavior of humps over time. Nonetheless, two-hump soliton launched under the same conditions results in large stationary single breather.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Mohd Hafiz Mohd, Rua Murray, Michael J. Plank, William Godsoe One of the important issues in ecology is to predict which species will be present (or absent) across a geographical region. Dispersal is thought to have an important influence on the range limits of species, and understanding this problem in a multi-species community with priority effects (i.e. initial abundances determine species presence-absence) is a challenging task because dispersal also interacts with biotic and abiotic factors. Here, we propose a simple multi-species model to investigate the joint effects of biotic interactions and dispersal on species presence-absence. Our results show that dispersal can substantially expand species ranges when biotic and abiotic forces are present; consequently, coexistence of multiple species is possible. The model also exhibits ecologically interesting priority effects, mediated by intense biotic interactions. In the absence of dispersal, competitive exclusion of all but one species occurs. We find that dispersal reduces competitive exclusion effects that occur in no-dispersal case and promotes coexistence of multiple species. These results also show that priority effects are still prevalent in multi-species communities in the presence of dispersal process. We also illustrate the existence of threshold values of competitive strength (i.e. transcritical bifurcations), which results in different species presence-absence in multi-species communities with and without dispersal.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Ranjit Kumar Upadhyay, Argha Mondal Bursting of neuronal firing is an interesting dynamical consequences depending on fast/slow dynamics. Certain cells in different brain regions produce spike-burst activity. We study such firing activity and its transitions to synchronization using identical as well as non-identical coupled bursting Morris-Lecar (M-L) neurons. Synchronization of different firing activity is a multi-time-scale phenomenon and burst synchronization presents the precursor to spike synchronization. Chemical synapses are one of the dynamical means of information processing between neurons. Electrical synapses play a major role for synchronous activity in a certain network of neurons. Synaptically coupled neural cells exhibit different types of synchronization such as in phase or anti-phase depending on the nature and strength of coupling functions and the synchronization regimes are analyzed by similarity functions. The sequential transitions to synchronization regime are examined by the maximum transverse Lyapunov exponents. Synchronization of voltage traces of two types of planar bursting mechanisms is explored for both kind of synapses under realistic conditions. The noisy influence effects on the transmission of signals and strongly acts to the firing activity (such as periodic firing and bursting) and integration of signals for a network. It has been examined using the mean interspike interval analysis. The transition to synchronization states of coupled and a network of bursting neurons may be useful for further research in information processing and even the origins of certain neurological disorders.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Sifeu Takougang Kingni, Viet-Thanh Pham, Sajad Jafari, Paul Woafo A three-dimensional autonomous chaotic system with an infinite number of equilibrium points located on a line and a hyperbola is proposed in this paper. To analyze the dynamical behaviors of the proposed system, mathematical tools such as Routh-Hurwitz criteria, Lyapunov exponents and bifurcation diagram are exploited. For a suitable choice of the parameters, the proposed system can generate periodic oscillations and chaotic attractors of different shapes such as bistable and monostable chaotic attractors. In addition, an electronic circuit is designed and implemented to verify the feasibility of the proposed system. A good qualitative agreement is shown between the numerical simulations and the Orcard-PSpice results. Moreover, the fractional-order form of the proposed system is studied using analog and numerical simulations. It is found that chaos, periodic oscillations and periodic spiking exist in this proposed system with order less than three. Then an electronic circuit is designed for the commensurate fractional order α = 0.98, from which we can observe that a chaotic attractor exists in the fractional-order form of the proposed system. Finally, the problem of drive-response generalized projective synchronization of the fractional-order form of the chaotic proposed autonomous system is considered.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Jun Ma, Ya Wang, Chunni Wang, Ying Xu, Guodong Ren Based on the Fitzhugh–Nagumo neuron model, the effect of electromagnetic induction is considered and external electromagnetic radiation is imposed to detect the mode transition of electrical activities in a myocardial cell. Appropriate dynamical and functional responses can be observed in the sampled series for membrane potentials by setting different feedback modulation on the membrane potential in presence of electromagnetic radiation. The electromagnetic radiation is described by a periodical forcing on the magnetic flux, and it is found that the response frequency can keep pace with the frequency of external forcing. However, mismatch of frequency occurs by further increasing the frequency of external forcing, it could account for the information encoding of neuron. The dynamical response could be associated with the magnetization and polarization of the media, thus the outputs of membrane potential can become quiescent and/or bursting as well.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Chenglin Li This paper is purported to investigate a cross-diffusion system arising in a predator-prey population model including Holling type-II functional response in a bounded domain with Dirichlet boundary condition. The asymptotical stabilities are investigated to this system by using the method of eigenvalue. Moreover, the existence of positive steady states are considered by using fixed points index theory, bifurcation theory, energy estimates and the differential method of implicit function.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Grzegorz Litak, Gabriel Abadal, Andrzej Rysak, Hubert Przywara We study dynamics of a micro-electro-mechanical system designed for energy harvesting. We explore bistability using an electrostatic system which is based on the repulsive interaction between two electrets. The system is composed of two micro cantilever beams locally charged in both tip free ends. Transition from a single potential well oscillations to cross-well motion is analysed. In particular, we analyse the effect of asymmetry in the potential wells and an escape phenomenon from the wells by using the Melnikov approach. The results were confirmed by numerical simulations.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Kamal N. Soltanov, Anatolij K. Prykarpatski, Denis Blackmore It is shown that members of a class (of current interest with many applications) of non-dissipative reaction-diffusion partial differential equations with local nonlinearity can have an infinite number of different unstable solutions traveling along an axis of the space variable with varying speeds, traveling impulses and also an infinite number of different states of spatio-temporal (diffusion) chaos. These solutions are generated by cascades of bifurcations governed by the corresponding steady states. The behavior of these solutions is analyzed in detail and, as an example, it is explained how space-time chaos can arise. Results of the same type are also obtained in the case of a nonlocal nonlinearity.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): S. Behnia, J. Ziaei According to the Anderson localization theory, the wavefunctions of a sufficiently strong disordered system are localized. We show that shifting hopping energy between nearest neighbors would induce an anomalous localization-delocalization transition in a disordered square lattice nanotube modelled by tight-binding. For this purpose, the consecutive level spacing statistics and the singularity spectrum analyses were performed. The quantum analysis of singularity spectrum reveals distinctive multifractality structures of the wavefunctions associated with localized and delocalized phases. We find that while in finite-size limit the system has a sudden metal-insulator transition, in large-scale limit the system experiences a rapid but continuous crossover. Interestingly, we report a critical value of hopping energy for which the system behavior is fairly close to metallic phase and especially independent of the system size. Passing this critical value, a great difference in the electronic transport properties of the system occurs. It follows that in the large-scale size, the system tends to follow semi-metallic behavior, while in finite size behaves more like to an insulator. The localization-delocalization transition is also reflected in the electrical current. In accordance with the indicators studied, we find that in delocalized regime there is a spreading electrical current throughout the whole system with an azimuthal symmetric characteristic.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Jagdev Singh, Devendra Kumar, Juan J. Nieto In this article, we analyze the El Nino–Southern Oscillation (ENSO) model in the global climate with a new fractional derivative recently proposed by Caputo and Fabrizio. We obtain the solution by using the iterative method. By using the fixed-point theorem the existence of the solution is discussed. A deeply analysis of the uniqueness of the solution is also discussed. And to observe the effect of the fractional order we presented some numerical simulations.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Zengshan Li, Diyi Chen, Mengmeng Ma, Xinguang Zhang, Yonghong Wu This paper demonstrates the existence of Feigenbaum's constants in reverse bifurcation for fractional-order Rössler system. First, the numerical algorithm of fractional-order Rössler system is presented. Then, the definition of Feigenbaum's constants in reverse bifurcation is provided. Third, in order to observe the effect of fractional-order to Feigenbaum's constants in reverse bifurcation, a series of bifurcation diagrams are computed. The Feigenbaum's constants in reverse bifurcation are measured and the error percentage in fractional-order Rössler system is presented. The simulation results show that Feigenbaum's constants exist in reverse bifurcation for fractional-order Rössler system. Especially, the Feigenbaum's constants still exist in the periodic windows. A summary on previous others’ works about Feigenbaum's constants is proposed. This paper draw a conclusion that the constants are universal in both period-doubling bifurcation and reverse bifurcation for both integer and fractional-order system.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Dongxi Li, Xiaowei Cui In this paper, we study the effect of stochastic noise on the virus infection model with nonlytic immune response. Firstly, the mathematical model describing the virus infection with nonlytic immune response is presented. The basic reproduction number is derived and the stability of disease-free state E 0 and disease state E 1 are analysed. Then the threshold conditions for extinction and persistence of the virus are derived by the rigorous theoretical proofs. It is found that when the noise is large enough, the virus will die out without constraint. When the noise is small, the virus will become extinct under the condition R 0 * < 1 and persistence under R 0 * * > 1 . Besides, the upper bound and lower bound for persistence have been given. At last, some numerical simulations are carried out to support our results. The conclusion of this paper could help provide the theoretical basis for the further study of the virus infection.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): M. Agaoglou, V.M. Rothos, H. Susanto An rf superconducting quantum interference device (SQUID) consists of a superconducting ring interrupted by a Josephson junction (JJ). The induced supercurrents around the ring are determined by the JJ through the celebrated Josephson relations. We study the dynamics of a pair of parametrically-driven coupled SQUIDs lying on the same plane with their axes in parallel. The drive is through the alternating critical current of the JJs. This system exhibits rich nonlinear behavior, including chaotic effects. We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture allows us to expose the existence of homoclinic orbits in the dynamics of the integrable part of the slow equations of motion. Using high-dimensional Melnikov theory, we are able to obtain explicit parameter values for which these orbits persist in the full system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to form so called Shilnikov orbits, indicating a loss of integrability and the existence of chaos.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): K. Berrada Recently, various quantum physical systems have been suggested to control the precision of quantum measurements. Here, we propose a useful quantum system to enhance the precision of the parameter estimation by investigating the problem of estimation in double quantum dot (DQD) spin qubits by considered a transmission line resonator (TLR) as a bus system. To do this, we study the dynamical variation of the quantum Fisher information (QFI) in this scheme including the influence of the different physical parameters. We show that the amount of QFI has a small decay rate in the time and it can be controlled by adjusting the magnetic coupling between DQDs via TLR, initial parameters, and detuning parameter between the qubit system and TLR. These features make DQDs via TLR good candidates for implementation of schemes of quantum computation and coherent information processing.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Guoyuan Qi, Jiangfeng Zhang The Qi chaotic system is transformed into a Kolmogorov-type system, thereby facilitating the analysis of energy exchange in its different forms. Regarding four forms of energy, the vector field of this chaotic system is decomposed into four forms of torque: inertial, internal, dissipative, and external. The rate of change of the Casimir function is equal to the exchange power between the dissipative energy and the supplied energy. The exchange power governs the orbital behavior and the cycling of energy. With the rate of change of Casimir function, a general bound and least upper bound of the Qi chaotic attractor are proposed. A detailed analysis with illustrations is conducted to uncover insights, in particular, cycling among the different types of energy for this chaotic attractor and key factors producing the different types of dynamic modes.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): E.S. Medeiros, I.L. Caldas, M.S. Baptista The sensitive dependence of periodicity and chaos on parameters is investigated for three-dimensional nonlinear dynamical systems. Previous works have found that noninvertible low-dimensional maps present power-law exponents relating the uncertainty between periodicity and chaos to the precision on the system parameters. Furthermore, the values obtained for these exponents have been conjectured to be universal in these maps. However, confirmation of the observed exponent values in continuous-time systems remain an open question. In this work, we show that one of these exponents can also be found in different classes of three-dimensional continuous-time dynamical systems, suggesting that the sensitive dependence on parameters of deterministic nonlinear dynamical systems is typical.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Zengyun Hu, Zhidong Teng, Tailei Zhang, Qiming Zhou, Xi Chen In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Guangxi Cao, Qi Zhang, Qingchen Li The foreign exchange (FX) market is a typical complex dynamic system under the background of exchange rate marketization reform and is an important part of the financial market. This study aims to generate an international FX network based on complex network theory. This study employs the mutual information method to judge the nonlinear characteristics of 54 major currencies in international FX markets. Through this method, we find that the FX network possesses a small average path length and a large clustering coefficient under different thresholds and that it exhibits small-world characteristics as a whole. Results show that the relationship between FX rates is close. Volatility can quickly transfer in the whole market, and the FX volatility of influential individual states transfers at a fast pace and a large scale. The period from July 21, 2005 to March 31, 2015 is subdivided into three sub-periods (i.e., before, during, and after the US sub-prime crisis) to analyze the topology evolution of FX markets using the maximum spanning tree approach. Results show that the USD gradually lost its core position, EUR remained a stable center, and the center of the Asian cluster became unstable. Liang's entropy theory is used to analyze the causal relationship between the four large clusters of the world.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Cristina Flaut, Vitalii Shpakivskyi, Elena Vlad In this paper, we introduce h(x) – Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K ( K = R , C ) . These polynomials generalize h(x) – Fibonacci quaternion polynomials andh(x) – Fibonacci octonion polynomials. For h(x) – Fibonacci polynomials in an arbitrary algebra, we provide generating function, Binet-style formula, Catalan-style identity, and d’Ocagne-type identity.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Shijian Cang, Aiguo Wu, Zenghui Wang, Zengqiang Chen Based on the generalized Hamiltonian system, a new method for constructing a class of three-dimensional (3-D) chaotic systems is presented in this paper. After choosing the proper parameters of skew-symmetric matrix, dissipative matrix and external input, one smooth 3-D chaotic system is proposed to show the effectiveness of the proposed method. Numerical simulation techniques, including phase portraits, Poincaré sections, Lyapunov exponents and bifurcation diagram, illustrate that the proposed 3-D system has periodic, quasi-periodic and chaotic flows under the conditions of different parameters.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): M.A. AL-Jawary This paper presents a new implementation of a reliable iterative method proposed by Temimi and Ansari namely (TAM) for approximate solutions of a nonlinear problem that arises in the thin film flow of a third grade fluid on a moving belt. The solution is obtained in the form of a series that converges to the exact solution with easily computed components, without any restrictive assumptions for nonlinear terms. The results are bench-marked against a numerical solution based on the classical Runge–Kutta method (RK4) and an excellent agreement is observed. Error analysis of the approximate solution is performed using the error remainder and the maximal error remainder. An exponential rate for the convergence is achieved. A symbolic manipulator Mathematica ®10 was used to evaluate terms in the iterative process.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): J. Alvarez-Ramirez, E. Rodríguez, J.C. Echeverría The rescaled range (R/S) analysis was used for analyzing the fractal scaling properties of heart rate variability (HRV) of subjects undergoing premeditation and meditation states. Eight novice subjects and four advanced practitioners were considered. The corresponding pre-meditation and meditation HRV data were obtained from the Physionet database. The results showed that mindfulness meditation induces a decrement of the HRV long-range scaling correlations as quantified with the time-variant Hurst exponent. The Hurst exponent for advanced meditation practitioners decreases up to values of 0.5, reflecting uncorrelated (e.g., white noise-like) HRV dynamics. Some parallelisms between mindfulness meditation and deep sleep (Stage 4) are discussed, suggesting that the former can be regarded as a type of induced deep sleep-like dynamics.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Jinhui Li, Zhidong Teng, Guangqing Wang, Long Zhang, Cheng Hu In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Fuzhong Nian, Song Ren, Zhongkai Dang In this paper, we constructed the virus propagation tree for any infected node through improving the k-shell decomposition method. Supposing we determine the position of infected nodes, the root node of the propagation tree is an infected node and its children nodes are susceptible nodes. The virus can be diffused from the bottom to top along with the tree. Based on the analysis of the virus propagation tree, a propagation-weighted priority immunization strategy was proposed to vaccinate the influential nodes(the nodes are the several nodes of the most risky in the high-risk node and it is convenient for us to immune). The mathematical proof and the computer simulation on scale-free network are given. The results show that the propagation-weighted priority immunization is effective to prevent the virus from diffusing.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Mauricio Gabriel-Guzmán, Victor M. Rivera, Yolanda Cocotle-Ronzón, Samuel García-Díaz, Eliseo Hernandez-Martinez The roasting is the stage where the coffee bean undergoes physiochemical changes that provide their typical sensory characteristics (i.e., aroma and flavor). Despite the importance, the roasting process is performed based on the operator experience, which makes difficult the homogenization between batches of roasted coffee. In that sense, this paper proposes a methodology to analyze changes in the coffee bean during roasting; this can be used as an indicator of the roasting degree. The proposal is based on R/S fractal analysis of coffee bean surface images taken during the roasting process. The results indicate that the Hurst exponent exhibits dynamic changes that can be correlated with the physical changes of the coffee bean, such as fractures and color changes, suggesting that the fractal index could be used for indirect monitoring of the roasting degree.