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): Martin Dlask, Jaromir Kukal Correlation dimension is one of the many types of fractal dimension. It is usually estimated from a finite number of points from a fractal set using correlation sum and regression in a log-log plot. However, this traditional approach requires a large amount of data and often leads to a biased estimate. The novel approach proposed here can be used for the estimation of the correlation dimension in a frequency domain using the power spectrum of the investigated fractal set. This work presents a new spectral characteristic called “rotational spectrum” and shows its properties in relation to the correlation dimension. The theoretical results can be directly applied to uniformly distributed samples from a given point set. The efficiency of the proposed method was tested on sets with a known correlation dimension using Monte Carlo simulation. The simulation results showed that this method can provide an unbiased estimation for many types of fractal sets.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Jie-Meng Zhang, Jin Chen, Ying-Jun Guo, Zhi-Xiong Wen In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by countable states automata. Moreover, we prove that the regularity of some regular sequences is invariant under some codings.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Liangqiang Zhou, Shanshan Liu, Fangqi Chen Using both analytical and numerical methods, global dynamics including subharmonic bifurcations and chaotic motions for a class of inverted pendulum system are investigated in this paper. The expressions of the heteroclinic orbits and periodic orbits are obtained analytically. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The conditions for subharmonic bifurcations are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Francisco J. Diaz-Otero, Omar Guillán-Lorenzo, Laura Pedrosa-Rodríguez We study the propagation properties of nonlinear pulses with periodic evolution in a dispersion-managed transmission link by means of a variational approach. We fit the energy enhancement required for stable propagation of a single soliton in a prototypical commercial link to a polynomial approximation that describes the dependence of the energy on the map strength of the normalized unit cell. We present an improvement of a relatively old and essential result, namely, the dependence of the energy-enhancement factor of dispersion-management solitons with the square of the map strength of the fiber link. We find that adding additional corrections to the conventional quadratic formula up to the fourth order results in an improvement in the accuracy of the description of the numerical results obtained with the variational approximation. Even a small error in the energy is found to introduce large deviations in the pulse parameters during its evolution. The error in the evaluation of the interaction distance between two adjacent time division multiplexed pulses propagating in the same channel in a prototypical submarine link is of the same order as the error in the energy.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Amin Jajarmi, Mojtaba Hajipour, Dumitru Baleanu This paper mainly focuses on the analysis of a hyperchaotic financial system as well as its chaos control and synchronization. The phase diagrams of the above system are plotted and its dynamical behaviours like equilibrium points, stability, hyperchaotic attractors and Lyapunov exponents are investigated. In order to control the hyperchaos, an efficient optimal controller based on the Pontryagin’s maximum principle is designed and an adaptive controller established by the Lyapunov stability theory is also implemented. Furthermore, two identical financial models are globally synchronized by using an interesting adaptive control scheme. Finally, a fractional economic model is introduced which can also generate hyperchaotic attractors. In this case, a linear state feedback controller together with an active control technique are used in order to control the hyperchaos and realize the synchronization, respectively. Numerical simulations verifying the theoretical analysis are included.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Christophe Letellier, Sourav Kumar Sasmal, Clément Draghi, Fabrice Denis, Dibakar Ghosh Combined therapy made of a chemotherapy and antiangiogenic agents is a clinical treatment recommended for its efficiency. Since the optimization of a treatment against cancer relasp is still mostly based on oncologist’s know-how, it is desirable to develop different approaches for such a task. Mathematical modelling is one of the promising ways. We here investigated the action of a combined therapy inserted to a mathematical cancer model in order to determine how the dynamics underlying tumor growth is governed by some key parameters. We here retained a chemotherapy (for instance, paclitaxel and carboplatin) combined with an antiangiogenic drug (as bevacizumab) applied to a cancer model describing the interactions between host, immune, tumor and endothelial cells. The effects of such a therapy are investigated and the relevant role played by the “normal” tissue of the tumor micro-environment is evidenced.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Vladimir García-Morales We introduce B κ -embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by κ, a finite or denumerable set of objects at κ = 0 (e.g. numbers, functions, vectors, coefficients of a generating function...) to their ordinary sum at κ → ∞. We show that B κ -embeddings can be used to design nonlinear irreversible processes through this connection. A number of examples of increasing complexity are worked out to illustrate the possibilities uncovered by this concept. These include not only smooth functions but also fractals on the real line and on the complex plane. As an application, we use B κ -embeddings to formulate a robust method for finding all roots of a univariate polynomial without factorizing or deflating the polynomial. We illustrate this method by finding all roots of a polynomial of 19th degree.

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): Kh. Lotfy In this paper, we consider a one dimensional problem of waves in a thermoelastic infinite medium with a spherical cavity. We are concerned with the study a new model of fractional order heat conduction law for a spherical cavity of a semiconductor medium. The governing equations are solved under the effect of the theory of coupled plasma, elastic, thermal waves through a photothermal process. The inner surface of the cavity is taken traction free with thermal shock. Time-dependence is removed by Laplace transform technique to governing equations. This method has been used to get the exact expression of some physical quantities, thermal activation coupling parameters and illustrated graphically.

Abstract: Publication date: June 2017 Source:Chaos, Solitons & Fractals, Volume 99 Author(s): Wencheng Guo, Jiandong Yang Based on the nonlinear mathematical model of the turbine regulating system of hydroelectric power plant with upstream surge chamber and sloping ceiling tailrace tunnel and the Hopf bifurcation theory, this paper firstly studies the dynamic performance of the turbine regulating system under 0.5 times Thoma sectional area of surge chamber, and reveals a novel dynamic performance. Then, the relationship between the two bifurcation lines and the wave superposition of upstream surge chamber and sloping ceiling tailrace tunnel is analyzed. Finally, the effect mechanisms of the wave superposition on the system stability are investigated, and the methods to improve the system stability are proposed. The results indicate that: Under the combined effect of upstream surge chamber and sloping ceiling tailrace tunnel, the dynamic performance of the turbine regulating system of hydroelectric power plant shows an obvious difference on the two sides of the critical sectional area of surge chamber. There are two bifurcation lines for the condition of 0.5 times Thoma sectional area, i.e. Bifurcation line 1 and Bifurcation line 2, which represent the stability characteristics of the flow oscillation of “penstock-sloping ceiling tailrace tunnel” and the water-level fluctuation in upstream surge chamber, respectively. The stable domain of the system is determined by Bifurcation line 2. The effect of upstream surge chamber mainly depends on its sectional area, while the effect of the sloping ceiling tailrace tunnel mainly depends on the sectional area of surge chamber, type of load disturbance and ceiling slope angle. When the stable domain is determined by Bifurcation line 1, the combined effect of upstream surge chamber and sloping ceiling tailrace tunnel on stability equals to the linear superposition of their own effects play alone. When the stable domain is determined by Bifurcation line 2, the only way to improve the system stability is to increase the sectional area of upstream surge chamber.

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.

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): Khalid Hattaf, Driss Riad, Noura Yousfi In this work, we propose a delayed business cycle model with general investment function. The time delays are introduced into gross product and capital stock, respectively. We first prove that the model is mathematically and economically well posed. In addition, the stability of the economic equilibrium and the existence of Hopf bifurcation are investigated. Our main results show that both time delays can cause the macro-economic system to fluctuate and the economic equilibrium to lose or gain its stability. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the normal form method and center manifold theory. Furthermore, the models and results presented in many previous studies are improved and generalized.

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): N. Kalamaras, K. Philippopoulos, D. Deligiorgi, C.G. Tzanis, G. Karvounis The aim of the current research study is to examine the scaling properties of the mean daily, maximum and minimum air temperature time series of a single coastal site, located at the island of Crete in Greece. The Multifractal Detrended Fluctuation Analysis (MF-DFA) is used to examine the time series long-term correlation and the singularity spectrum to estimate the multifractality degree. The analysis reveals that the daily temperature time series exhibit a multifractal behavior, are positive long-term correlated and that their multifractal structure is insensitive to local fluctuations with large magnitudes.

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): Mobin Kavyanpoor, Saeed Shokrollahi In this letter, a solution of the fractional Van Der Pol equation that uses the differential transform method has been investigated. In previous studies this method was incorrectly applied to the fractional Van Der Pol oscillator and inaccurate results were obtained. In this note, true solution of the problem has been presented. Although it was shown that, this method is not appropriate and a non-periodic solution was obtained.

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): Hyonhui Ju, Cholsan Kim, Yunmi Choe, Minghao Chen Let X be a compact metric space and f: X → X be a continuous map. In [14], it was shown that if a dynamical system (X, f) has strictly coupled-expanding property, then the Hyperspace dynamical system ( K ( X ) , f ¯ ) , induced by (X, f), has a subsystem which is topologically semi-conjugated to a full shift (Σk, σ). In this paper, we show that under some conditions more weaker than those of [14], ( K ( X ) , f ¯ ) has a subsystem which not only is topologically semi-conjugated to a subshift of finite type (ΣA, σA ), but also is bigger than the subsystem builded in [14]. Furthermore, we expand above results to the fuzzy dynamical system, extended by (X, f).

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): Peng Liu, Xijun Liu Considering the targeted chemotherapy, a mathematical model of tumor-immune system was constructed on the basis of de Pillis’s model. In this paper, we conducted qualitative analysis on the mathematical model, including the positivity and boundedness of solutions, local stability and global stability of equilibrium solutions. Some numerical simulations were given to illustrate the analytic results. Comparing the targeted chemotherapy model with regular chemotherapy model, we found that the targeted chemotherapy was benefit to kill tumor cells.

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): Cong Wang, Hong-li Zhang, Wen-hui Fan In this paper, we propose a new method to improve the safety of secure communication. This method uses the generalized dislocated lag projective synchronization and function projective synchronization to form a new generalized dislocated lag function projective synchronization. Moreover, this paper takes the examples of fractional order Chen system and Lü system with uncertain parameters as illustration. As the parameters of the two systems are uncertain, the nonlinear controller and parameter update algorithms are designed based on the fractional stability theory and adaptive control method. Moreover, this synchronization form and method of control are applied to secure communication via chaotic masking modulation. Many information signals can be recovered and validated. Finally, simulations are used to show the validity and feasibility of the proposed scheme.

Abstract: Publication date: May 2017 Source:Chaos, Solitons & Fractals, Volume 98 Author(s): Chunrui Zhang, Zhenzhang Sui, Hongpeng Li Network with interacting loops and time delays are common in physiological systems. In the past few years, the dynamic behaviors of coupled interacting loops neural networks have been widely studied due to their extensive applications in classification of pattern recognition, signal processing, image processing, engineering optimization and animal locomotion, and other areas, see the references therein. In a large amount of applications, complex signals often occur and the complex-valued recurrent neural networks are preferable. In this paper, we study a complex value Hopfield-type network that consists of a pair of one-way rings each with four neurons and two-way coupling between each ring. We discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. The existence of multiple branches of bifurcating periodic solution is obtained. We also found that the spatio-temporal patterns of bifurcating periodic oscillations alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond to different patterns of neural network oscillators. The oscillations of corresponding neurons in the two loops can be in phase or anti-phase depending on the parameters and delay. Some numerical simulations support our analysis results.