Authors:Mahmoud Moustafa; Mohd Hafiz Mohd; Ahmad Izani Ismail; Farah Aini Abdullah Pages: 1 - 13 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Mahmoud Moustafa, Mohd Hafiz Mohd, Ahmad Izani Ismail, Farah Aini Abdullah This paper considers a fractional order Rosenzweig-MacArthur (R-M) model incorporating a prey refuge. The model is constructed and analyzed in detail. The existence, uniqueness, non-negativity and boundedness of the solutions as well as the local and global asymptotic stability of the equilibrium points are studied. Sufficient conditions for the stability and the occurrence of Hopf bifurcation for the fractional order R-M model are demonstrated. The resolution of the paradox of enrichment is investigated. The impact of fractional order and the prey refuge effects on the stability of the system are also studied both theoretically and by using numerical simulations.
Authors:H. Ramezannejad Azarboni; R. Ansari; A. Nazarinezhad Pages: 14 - 25 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): H. Ramezannejad Azarboni, R. Ansari, A. Nazarinezhad In this article, the nonlinear chaotic and periodic dynamic responses of doubly curved functionally graded shallow shells subjected to harmonic external excitation are numerically investigated. Material characteristics of the shell are defined according to a simple power law distribution through the thickness. Based on the first-order shear deformation shell theory and using the Donnell nonlinear kinematic relations the set of the governing equations are derived. The Galerkin method together with trigonometric mode shape functions is applied to solve the equations of motion. Also, the nonlinearly coupled time integration of the governing equation of plate is solved employing fourth-order Runge–Kutta method. The effects of amplitude and frequency of external force on the nonlinear dynamic response of shells are investigated. The bifurcation diagram and largest Lyapunov exponent are employed to detect the amplitude and frequency of external force critical parameter of periodic and chaotic response of shallow shells under periodic force. Having known the critical values, phase portrait, Poincare maps, time history and power spectrum are presented to observe the periodic and chaotic behavior of the system.
Authors:Yuhan Zhang; Xin Feng; Ye Wu; Jinghua Xiao Pages: 26 - 30 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Yuhan Zhang, Xin Feng, Ye Wu, Jinghua Xiao Nowadays online consumer reviews (OCR) has increasingly received scholars' attention as an important form of word-of-mouth. Recent study shows that online reviews of a product, such as a book or a restaurant, have effect on long-term consuming behavior and the future rating of the product, it mainly reflects that the early high rating of a product will lead the decrease trend of rating over time. To confirm the existence of the effect and explore how it works, over 180,000 reviews on Dianping.com were collected to investigate the behavior patterns and intrinsic dynamics. In this paper, four temporal evolution patterns were observed via evaluating the cumulative average rating series for each restaurant. Moreover, a conceptual model considering the influence of heterogeneous preferences and the self-selection mechanism was introduced, and the numerical results coincided with the empirical analysis well enough to support the hypotheses. We find special preferences result in tendentious consumption and unrepresentative reviews, these reviews lead the potential consumers to over- or under-estimate the products and directly affect the subsequent ratings. The conclusions of this paper can contribute to the specific policies to adjust the initial rating effect for the specific marketing strategies.
Authors:Gleison F.V. Amaral; Erivelton G. Nepomuceno Pages: 31 - 35 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Gleison F.V. Amaral, Erivelton G. Nepomuceno This paper reports a smooth-piecewise model to the Cord Attractor. The fact that the Cord Attractor has one real fixed point and two complex conjugate fixed points does not allow to use a technique based on the building of two affine subsystems, which requires at least two real fixed points [Chaos 16, 013115 (2006)]. In this work, we have presented a procedure to at least partially overcome this limitation using a virtual fixed point; the location of the fixed point is based on the topology of the original system. The switching function has been designed as a smooth function. The phase space and the local-finite largest Lyapunov exponent have been used to compare the resulting attractor with the original Cord Attractor.
Authors:Bo Gao; Xuan Liu; Zhongzhou Lan; Rongrong Fu Pages: 36 - 40 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Bo Gao, Xuan Liu, Zhongzhou Lan, Rongrong Fu Non-Linear Feedback Shift Registers (NFSRs) are a generalization of Liner Feedback Shift Registers (LFSRs). The study of NFSR sequence helps to analyze the cryptographical security of NFSR-based stream cipher. Due to lack of efficient algebraic tools, the period of NFSR still remains an open crucial theoretical problem. In this paper, we view the NFSR as a Boolean network (BN), so that the study about the period of NFSR can be viewed as the study about period of BN. Furthermore, based on the mathematical tool of semi-tensor product (STP), a Boolean network can be mapped into an algebraic form. For these, we put forward a method for reconstructing the period of NFSR with single input. Especially, we propose a procedure to choose the controlled states and steer the controlled states from initial state to desirable one. At last, the general derivation is exemplified by numerical simulations for a kind of NFSR.
Authors:Zhenghong Deng; Yijie Huang; Zhiyang Gu; Zhilong Deng; Jiwei Xu Pages: 41 - 46 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Zhenghong Deng, Yijie Huang, Zhiyang Gu, Zhilong Deng, Jiwei Xu In the real life, we often simultaneously encounter various social dilemmas, which are also inclined to be voluntarily participated in, instead of previous assumption's compulsory participation in. Accounting on this realistic scenario, we have introduced the mechanism that the individuals have access to different payoff matrices corresponding to different social dilemmas to participate in the multigame with three strategies to choose, including cooperation, defection, going it alone. Furthermore, we set a proportion ψ/2 of the population to play the Prisoner's Dilemma, a proportion ψ/2 of the population to play Snowdrift and a proportion 1 − ψ of the population to play the weak Prisoner's Dilemma, which results in the fact that the mean payoff matrix returns to the basic weak PD. Though numerical simulations, we find that for the smaller temptation to defect, the cooperation can be enhanced by the diversity of the sucker's payoff in the multigame contrast to the basic case. In addition, when the contribution of sucker's payoff is larger or more players choose to play the Prisoner's Dilemma and Snowdrift, the cooperators become more dominated.
Authors:Li-xin Yang; Jun Jiang Pages: 47 - 52 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Li-xin Yang, Jun Jiang This paper is devoted to synchronization analysis of the fractional order drive-response complex network. Firstly, a fractional order drive-response networks model with in-commensurate orders is proposed. Moreover, on the basis of the stability theory of linear fractional-order differential equations and open-loop strategy, we derive a sufficient condition for the stability of the modified projective synchronization behavior in such drive-response complex network. Furthermore, we verify our theoretical results by numerical simulations of drive-response complex network with in-commensurate orders.
Authors:H. Kaveh; H. Salarieh; R. Hajiloo Pages: 53 - 57 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): H. Kaveh, H. Salarieh, R. Hajiloo In this paper, a new approach to control continuous time chaotic systems with an unknown governing equation and limitation on the measurement of states, has been investigated. In many chaotic systems, disability to measure all of the states is a usual limitation, like in some economical, biological and many other engineering systems. Takens showed that a chaotic attractor has an astonishing feature in which it can embed to a mathematically similar attractor by using time series of one of the states. The new embedded attractor saves much information from the original attractor. This phenomenon has been deployed to present a new way to control continuous time chaotic systems, when only one of the states of the system is measurable and the system model is not also available.
Authors:Alexey Zhokh; Peter Strizhak Pages: 58 - 63 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Alexey Zhokh, Peter Strizhak In the present paper, Thiele modulus (TM) for a catalytic reaction with the anomalous diffusion of a reagent in a catalyst pellet is introduced. Different cases of the TM are considered related to the anomalous diffusion process governed by a diffusion equation with the space-fractional, time-fractional, and space-time fractional derivatives. In addition, each fractional derivative is used according to the Caputo and the Riemann–Liouville definitions. Closed-form expressions of the TM for each definition of the fractional derivative are provided. For the time-fractional derivative, the TM is obtained under the assumption of the reaction dynamics nonlinearity. We demonstrate and critically discuss the applicability of the TM obtained for the reaction-diffusion equation with non-integer order derivatives to the evaluation of the parameters of the heterogeneous catalytic process.
Authors:Sergio Bianchi; Augusto Pianese Pages: 64 - 75 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Sergio Bianchi, Augusto Pianese The increasing empirical evidence against the paradigm that stock markets behave efficiently suggests to relax the too restrictive dichotomy between efficient and inefficient markets. Starting from the idea that financial prices evolve in a continuum of equilibria and disequilibria, we use the Hurst–Hölder exponent to quantify the pointwise degree of (in)efficiency and introduce the notion of α-efficiency. We then define and study the properties of two functions which are used to build indicators providing timely information about the market efficiency. We apply our tools to the analysis of four stock indexes representative of U.S., Europe and Asia.
Authors:Chunbiao Li; Julien Clinton Sprott; Tomasz Kapitaniak; Tianai Lu Pages: 76 - 82 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Chunbiao Li, Julien Clinton Sprott, Tomasz Kapitaniak, Tianai Lu By introducing trigonometric functions in a 4-D hyperchaotic snap system, infinite 1-D, 2-D, and 3-D lattices of hyperchaotic strange attractors were produced. Furthermore a general approach was developed for constructing self-reproducing systems, in which infinitely many attractors share the same Lyapunov exponents. In this case, cumbersome constants are necessary to obtain offset boosting; correspondingly additional periodic functions are needed for attractor hatching. As an example, a hyperchaotic system with a hidden attractor was transformed for reproducing 1-D, 2-D infinite lattices of hyperchaotic attractors and a 4-D lattice of chaotic attractors.
Authors:İzzet Göksel; Nalan Antar; İlkay Bakırtaş Pages: 83 - 89 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): İzzet Göksel, Nalan Antar, İlkay Bakırtaş In this paper, we discuss the existence of lattice solitons supported by cubic-saturable nonlinearity in the framework of nonlinear Schrödinger (NLS) equation with external potentials such as parity-time-symmetric lattices with and without defects by using the pseudo-spectral renormalization method. Linear and nonlinear stability properties of the lattice solitons centered on the maximum of the PT -symmetric potential are investigated in detail.
Authors:Zhong Du; Bo Tian; Han-Peng Chai; Yan Sun; Xue-Hui Zhao Pages: 90 - 98 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Zhong Du, Bo Tian, Han-Peng Chai, Yan Sun, Xue-Hui Zhao In this paper, investigation is made on the coupled variable-coefficient fourth-order nonlinear Schrödinger equations, which describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Via the generalized Darboux transformation, the first- and second-order rogue wave solutions are constructed. Based on such solutions, effects of the group velocity dispersion coefficient and the fourth-order dispersion coefficient on the rogue waves are graphically analyzed. The first-order rogue waves with the eye-shaped distribution, the interactions between the first-order rogue waves with solitons, and the second-order rogue waves with one highest peak and with the triangular structure are displayed. When the value of the group velocity dispersion coefficient or the fourth-order dispersion increases, range of the first-order rogue wave increases. Composite rogue waves are obtained, where the temporal separation between two adjacent rogue waves can be changed if we adjust the group velocity dispersion coefficient and fourth-order dispersion coefficient. Periodic rogue waves are presented. Periods of such rogue waves decrease with the periods of the group-velocity dispersion and fourth-order dispersion coefficient decreasing.
Authors:Hiroaki S. Yamada Pages: 99 - 106 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Hiroaki S. Yamada We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition (SNCT). The energy sequences in question might be characterized by their correlation parameter B and the potential strength W. The quantum states resulting from such sequences have been characterized in the two ways: Lyapunov exponent at band centre and the dynamics of the initially localized wavepacket. Specifically, the B − dependence of the relevant Lyapunov exponent’s decay is changing from linear to exponential one around the SNCT (B ≃ 2). Moreover, here we show that even in the nonstationary regime, mean square displacement (MSD) of the wavepacket is noticeably suppressed in the long-time limit (dynamical localization). The B − dependence of the dynamical localization lengths determined by the MSD exhibits a clear change in the functional behaviour around SNCT, and its rapid increase gets much more moderate one for B ≥ 2. Moreover we show that the localization dynamics for B > 3/2 deviates from the one-parameter scaling of the localization in the transient region.
Authors:T. Akinaga; S.C. Generalis; F.H. Busse Pages: 107 - 117 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): T. Akinaga, S.C. Generalis, F.H. Busse The analysis of the Taylor-Couette problem in the small gap limit is extended to the cases of tertiary and quaternary solutions. The theoretical results are compared with experimental observations. Although in the latter the small-gap approximation is not always well approximated, the comparison of theoretical results and observations yields reasonable agreements. The absence of the wavy twist mode in the observed patterns is explained by the presence of no-slip boundary conditions in the axial direction of the experimental apparatus, which differ from the periodic conditions imposed in the theoretical analysis. Quaternary solutions bifurcating from the tertiary ones through subharmonic instabilities are presented and compared with experimental observations. Reasonable agreement has been found.
Authors:Mohamed Laib; Jean Golay; Luciano Telesca; Mikhail Kanevski Pages: 118 - 127 Abstract: Publication date: April 2018 Source:Chaos, Solitons & Fractals, Volume 109 Author(s): Mohamed Laib, Jean Golay, Luciano Telesca, Mikhail Kanevski In this paper, we applied the multifractal detrended fluctuation analysis to the daily means of wind speed measured by 119 weather stations distributed over the territory of Switzerland. The analysis was focused on the inner time fluctuations of wind speed, which could be linked with the local conditions of the highly varying topography of Switzerland. Our findings point out to a persistent behaviour of almost all measured wind speed series (indicated by a Hurst exponent larger than 0.5), and to a high multifractality degree indicating a relative dominance of the large fluctuations in the dynamics of wind speed, especially on the Swiss Plateau, which is comprised between the Jura and Alps mountain ranges. The study represents a contribution to the understanding of the dynamical mechanisms of wind speed variability in mountainous regions.
Authors:Huijuan Xie; Yubing Gong; Baoying Wang Pages: 1 - 7 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Huijuan Xie, Yubing Gong, Baoying Wang In this paper, we numerically study the effect of spike-timing-dependent plasticity on multiple coherence resonance and synchronization transitions induced by autaptic time delay in adaptive scale-free Hodgkin–Huxley neuron networks. As the adjusting rate Ap of spike-timing-dependent plasticity increases, multiple coherence resonance and synchronization transitions enhance and become strongest at an intermediate Ap value, indicating that there is optimal spike-timing-dependent plasticity that can most strongly enhance the multiple coherence resonance and synchronization transitions. As Ap increases, increasing network average degree has a small effect on multiple coherence resonance, but its effect on synchronization transitions changes from suppressing to enhancing it. As network size is varied, multiple coherence resonance and synchronization transitions nearly do not change. These results show that spike-timing-dependent plasticity can simultaneously optimize multiple coherence resonance and synchronization transitions by autaptic delay in the adaptive scale-free neuronal networks. These findings provide a new insight into spike-timing-dependent plasticity and autaptic delay for the information processing and transmission in neural systems.
Authors:Peiming Shi; Haifeng Xia; Dongying Han; Rongrong Fu; Danzhen Yuan Pages: 8 - 14 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Peiming Shi, Haifeng Xia, Dongying Han, Rongrong Fu, Danzhen Yuan Stochastic resonance (SR) in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise is investigated in this paper. First, the effective potential function is deduced based on probability density approach theory, small delay approximation theory and colored noise approximation theory. Second, the mean first-passage time (MFPT) which plays an important role in investigating on particles escape rate is derived and we find that the effect of additive color noise is more observable than that of multiplicative white noise on MFPT. Finally, influences of different parameters on SR are studied by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three-dimensional graphs of SNR with different parameters are obtained. We conclude that time delay τ and time delay strength e can suppress SR and that asymmetric item r has a non-monotone effect on SR. The results also suggest that adjusting the additive noise intensity Q is more sensitive than that of the multiplicative noise intensity D in controlling SNR.
Authors:Ge Zhang; Chunni Wang; Faris Alzahrani; Fuqiang Wu; Xinlei An Pages: 15 - 24 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Ge Zhang, Chunni Wang, Faris Alzahrani, Fuqiang Wu, Xinlei An Synapse is an important bridge for receiving and encoding signals, and the description for synapse current is critical for further signal processing. This paper investigates the dynamical characteristic in isolated neuron and chain neuronal networks with memristive autapse or synapses, respectively. Autapse plays important role in modulating the electrical activities, and thus the information encoding is enhanced. Within the improved neuron model, memristor is used to map the modulation of synapse current. Within an isolated new neuron model with memory, the modes in electrical activities can be controlled by the synapse current completely. Bifurcation analysis is carried out and mode transition is discussed. Furthermore, the modulation of synapse current on chain network is investigated, and the dependence of wave propagation on intensity of synapse is discussed. The diversity in synapse current can suppress the synchronization approach on the network.
Authors:K. Usha; P. A. Subha; Chitra R. Nayak Pages: 25 - 31 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): K. Usha, P. A. Subha, Chitra R. Nayak Network of coupled oscillators exhibit different types of spatiotemporal patterns. We report that as the coupling strength increases the unidirectionally coupled Hindmarsh–Rose neuron star network will synchronize. The condition for synchronization has been evaluated using Lyapunov function method. We also discuss the dynamics of the system in the presence of controllers. The control input generate interesting behaviors which consist of clusters of spatially coherent domains depending on the coupling strength. Drum head mode, mixed oscillatory state, desynchrony, and multi cluster states are formed and cluster reduction takes place before settling to complete synchrony. The evolution of a perfectly synchronized state via drum head mode, mixed oscillatory state, and clusters from a desynchronized state is reported for the first time. The parameter values which lead to stable cluster formation is also discussed. Our results suggest that in the presence of controllers the common oscillator in the star network behaves as a driver and generates the transitions and cluster formation acts as a precursor to complete synchrony in Hindmarsh–Rose model with unidirectional star coupling.
Authors:Aman Dhiman; Swarup Poria Pages: 32 - 38 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Aman Dhiman, Swarup Poria Cyclic dominance is observed in predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations and many other natural systems. Rock-Paper-Scissor(RPS) is a popular game which demonstrates cyclic dominance. In this paper, we investigate replicator dynamics of RPS-game under logistic growth functions with Allee effect. The results obtained are compared with the case of no Allee effect. Due to Allee effect the number of stable attractors increases in a certain parameter region. The obtained result can be interpreted biologically that diversity of an ecological system increases due to Allee effect.
Authors:Yong-Ki Ma; P. Prakash; A. Deiveegan Pages: 39 - 48 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Yong-Ki Ma, P. Prakash, A. Deiveegan In this paper, we identify the unknown space-dependent source term in a time-fractional diffusion equation with variable coefficients in a bounded domain where additional data are consider at a fixed time. Using the generalized and revised generalized Tikhonov regularization methods, we construct regularized solutions. Convergence estimates for both methods under an a-priori and a-posteriori regularization parameter choice rules are given, respectively. Numerical example shows that the proposed methods are effective and stable.
Authors:Chuan Chen; Lixiang Li; Haipeng Peng; Jürgen Kurths; Yixian Yang Pages: 49 - 56 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Chuan Chen, Lixiang Li, Haipeng Peng, Jürgen Kurths, Yixian Yang In this paper, we study the fixed-time synchronization of hybrid coupled networks, which have only one transmittal delay in the delayed coupling terms. The settling time of fixed-time synchronization can be adjusted to some desired values in advance regardless of the initial conditions. By constructing suitable Lyapunov functions and designing delay-dependent feedback controllers, we derive several novel synchronization criteria, which guarantee the considered hybrid coupled networks can achieve fixed-time synchronization. Two numerical examples are given to show the effectiveness of our results.
Authors:Xianhuan Chen; Chengyi Xia; Jin Wang Pages: 57 - 65 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Xianhuan Chen, Chengyi Xia, Jin Wang Mining the community structure is an important subject in the area of social network analysis, and detecting the hidden communities within the social networks will help to better understand the topological properties of the real-life networks. Meanwhile, community detection will be also helpful to monitor the public opinion, identify the opinion leaders and perform the personalized recommendation. In comparison with the simplex user ties or contents, considering the trust features from multiple users will provide a more comprehensive account of the linking relationship between users. To this end, we propose a novel non-overlapping community detection algorithm, which is based on the trust mechanism, to recognize the community structure in this paper. At first, we propose several definitions with regard to trust relationship between users to depict the trust strength, which includes the direct, indirect and mutual trust, and then the specific trust calculation method is provided to quantitatively describe the extent of trust. Secondly, starting from the trust relationship, we integrate the edge fitness and community fitness into the non-overlapping community detection and propose a novel trust-based algorithm to comprehensively leverage the trust among nodes to further mine the communities within the networks. Finally, to deeply analyze the analyze the performance, we take use of Lesmis and Gemo data sets to carry out extensive experiments, and the results show that, compared with other classical algorithms, the community based on the newly proposed algorithm features the higher trust cohesion on the condition that the structural cohesiveness of social network is fully satisfied. The current methods will be of significance to deeply understand and effectively find out the communities within realistic networks.
Authors:Deming Mao; Zhenxi Niu Pages: 66 - 70 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Deming Mao, Zhenxi Niu The compassionate behavior is present throughout the human society, and rich people always could not help having sympathy for poor individual. Inspired by this fact, we consider a donation model to describe the emergency and maintenance of cooperation with voluntary participate in spatial prisoner's dilemma game and we study this model on a square lattice. In detail, when the focal player has the least income in the group which includes his nearest four neighbors and himself, one of his neighbors who has the highest income will donate some proportion of his extra money to him. On the other hand, if focal individual is not the poorest, he will donate some incomes to his poorest neighbor. Through numeric simulation, we conclude that our donation model can promote the evolution of cooperation monotonously. Especially, the larger proportion payoff rich people can contribute, the higher level of cooperation we can get.
Authors:V.P. Tsvetkov; S.A. Mikheyev; I.V. Tsvetkov Pages: 71 - 76 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): V.P. Tsvetkov, S.A. Mikheyev, I.V. Tsvetkov The paper is devoted to the study of cardiac rhythm variability (CRV) using the phase and extended phase spaces of instantaneous cardiac rhythm (ICR) obtained from the Holter monitoring (HM) data. In order to construct these spaces, a software package is developed and implemented. With specific references, the fractality of the ICR phase space is demonstrated. The fractal phase space volume and fractal entropy definitions of ICR are given. The paper justifies their availability for CRV quantitative assessment.
Authors:Hengchun Hu; Yueyue Li; Haidong Zhu Pages: 77 - 81 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Hengchun Hu, Yueyue Li, Haidong Zhu The residual symmetries for the third-order Burgers equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables and the corresponding finite transformations are computed directly. New exact solutions of the third-order Burgers equation is also proved to have the consistent tanh expansion form. New exact interaction excitations such as soliton-cnoidal wave solutions and soliton-periodic wave solutions are given out analytically and graphically.
Authors:April Pease; Korosh Mahmoodi; Bruce J. West Pages: 82 - 86 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): April Pease, Korosh Mahmoodi, Bruce J. West We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes, with the interesting result that the complexity index of the crucial events is μ ≈ 2, which is the same inverse power-law index of the dynamics of the brain. The search technique analyzes music volume and confirms the results of the earlier work, thereby contributing to the explanation as to why the brain is sensitive to music, through the phenomenon of complexity matching. Complexity matching has recently been interpreted as the transfer of multifractality from one complex network to another. For this reason we also examine the mulifractality of music, with the observation that the multifractal spectrum of a computer performance is significantly narrower than the multifractal spectrum of a human performance of the same musical score. We conjecture that although crucial events are demonstrably important for information transmission, they alone are not sufficient to define musicality, which is more adequately measured by the multifractality spectrum.
Authors:Zheng-Hong Deng; Ji-Wei Xu; Xue-Qiang Li; Feng Huang Pages: 87 - 93 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Zheng-Hong Deng, Ji-Wei Xu, Xue-Qiang Li, Feng Huang Smart antenna can effectively suppress multipath interference, co-channel interference, and improves the transmission quality of signal and the utilization of spectrum, so it is widely applied in wireless communication network. To explore the optimization problem about smart antenna receiving array and sensor network which exists in radar, sonar and other systems, here we presents a kind of adaptive beam-forming algorithm based on diagonal-loading and mean square error (MSE) criterion. Such a novel algorithm could give the optimal solution of weight direction vector, and at the same guarantees its own robustness. Furthermore, it also possesses the advantage of shortening the convergence time of weight direction vector, and decreasing the sensitive issue of model error in high SNR environment. In our simulation experiments, it is shown that the proposed algorithm improves the performance of receiver network in sonar system, and to a certain extent achieves the signal optimization.
Authors:David Lambert; Fabio Vanni Pages: 94 - 103 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): David Lambert, Fabio Vanni We present an approximate analytical solution for the connectivity of a network model with a “non-simultaneous” linking scheme. This model exhibits node-space correlations in the link distribution, anomalous fluctuations in the time series of the connectivity variable, and a finite-size effect: the maximum number of links occurs away from the critical value of the system parameter. We derive an exact Master Equation for this model in the form of an infinitesimal time-evolution operator. Fluctuations are much more important than the mean-field approximation predicts, which we attribute to the heterogeneity in the model. Finally, we give a sketch of possible real world applications where the value of a network is related to the number of links.
Authors:Manseob Lee Pages: 104 - 106 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Manseob Lee In this paper, we show that C 1 generically, a vector field X has zero topological entropy if there are a C 1 neighborhood U of X and d > 0 such that for every Y ∈ U and a periodic point p of Y, ∥ P π ( p ) Y N p ∥ < π ( p ) d , where π(p) is the period of p, and PY is the linear Poincaré flow associated to Y. This result is a generalization of Arbieto and Morales [1].
Authors:I. Jaradat; M. Al-Dolat; K. Al-Zoubi; M. Alquran Pages: 107 - 110 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): I. Jaradat, M. Al-Dolat, K. Al-Zoubi, M. Alquran The latent potentialities and applications of fractional calculus present a mathematical challenge to establish its theoretical framework. One of these challenges is to have a compact and self-contained fractional power series representation that has a wider application scope and allows studying analytical properties. In this letter, we introduce a new more general form of fractional power series expansion, based on the Caputo sense of fractional derivative, with corresponding convergence property. In order to show the functionality of the proposed expansion, we apply the corresponding iterative fractional power series scheme to solve several fractional (integro-)differential equations.
Authors:H.A. Eiselt Pages: 111 - 118 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): H.A. Eiselt This paper uses a three-phase process to first describe the development of a network to describe different types of relations between terrorists and their supporters. It continues to review some of the usual measures of social network analysis to evaluate different positions in the network. Finally, the work describes different methods to destabilize the terrorist network, and, based on sensitivity analyses, determines the potential of certain actions and the vulnerability of the network.
Authors:Juliano A. de Oliveira; Larissa C. N. Ramos; Edson D. Leonel Pages: 119 - 122 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Juliano A. de Oliveira, Larissa C. N. Ramos, Edson D. Leonel We derived explicit forms for the convergence to the steady state for a 1-D Smith–Slatkin mapping at and near at bifurcations. We used a phenomenological description with a set of scaling hypothesis leading to a homogeneous function giving a scaling law. The procedure is supported by numerical simulations and confirmed by a theoretical description. At the bifurcation we used an approximation transforming the difference equation into a differential one whose solution remount all scaling features. Near the bifurcation an investigation of fixed point stability leads to the decay for the stationary state. Simulations are made in the pitchfork, transcritical and period doubling bifurcations.
Authors:Tahir Khan; Amir Khan; Gul Zaman Pages: 123 - 128 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Tahir Khan, Amir Khan, Gul Zaman We discuss the dynamic of a stochastic hepatitis B epidemic model. A stochastic hepatitis B model is formulated with a varying population environment for a long term behavior. The proposed model consists of three classes, namely the susceptible individuals in which the transmission rate is distributed by white noise, the infected individuals in which the same perturbation occurs and the recovered individuals. We derive sufficient conditions for the extinction and the persistence. Finally, we carry out the numerical simulations to support our analytical results.
Authors:Antoni Ferragut; Claudia Valls; Carsten Wiuf Pages: 129 - 135 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Antoni Ferragut, Claudia Valls, Carsten Wiuf We consider Edelstein’s dynamical system of three reversible reactions in R 3 and show that it is not Liouville (hence also not Darboux) integrable. To do so, we characterize its polynomial first integrals, Darboux polynomials and exponential factors.
Authors:Wang Jun; Luo Yuyan; Tang Lingyu; Ge Peng Pages: 136 - 147 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Wang Jun, Luo Yuyan, Tang Lingyu, Ge Peng Tourism demand forecasting is essential for forward tourism planning. To develop appropriate public policies and ensure sound business investment decisions, both government administrations and private sector businesses use basic tourist demand forecasting to plan future operations and assess the need for facilities and infrastructure investment. Therefore, forecasting has become indispensable to tourism management. This study proposes a combined tourism forecasting model using an artificial neural network (ANN) and a clustering algorithm, which considers two aspects of the given data series: sequence patterns and near characteristics, which embody structural changes and time series correlations. Training data were clustered into homogenous groups, and for each cluster, a dedicated forecaster was employed. Several neighboring samples were then selected to capture the current changes in the data series trends. Finally, the two prediction results derived from the sequence patterns and near characteristics were combined to determine the final forecast results. To verify the superiority and accuracy of the proposed model, it was compared with three other ANN-based models and the most popular ARIMA model using three non-linear, non-stationary tourist arrivals data series. Experimental cases studies demonstrated that the proposed combination method consistently outperformed the other related methods.
Authors:Hong-Tao Zhang; Li Li Pages: 148 - 153 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Hong-Tao Zhang, Li Li In this paper, we present a single species model with cannibalism and nonlocal effect. The existence of traveling wave fronts connecting the equilibrium 0 to the equilibrium K r r + K h is proved when the wave speed c ≥ 2 r .
Authors:Asaf Khan; Gul Zaman Pages: 154 - 165 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Asaf Khan, Gul Zaman In the present study, an age-structured SEIR endemic model is considered. The population is assumed to be not constant due to different inflows and outflows that are imbalanced by demographics, and migration etc. An abstract Cauchy problem is formulated from the model in order to show that the model is well-posed. The local and global stability of the disease-free steady state is examined using the basic reproduction number R 0. Under certain condition, the endemic steady state is shown to be exist and locally stable. To illustrate the main theorems, sample simulations are presented at the end of the paper.
Authors:Kang-Kang Wang; Lin Ju; Ya-Jun Wang; Sheng-Hong Li Pages: 166 - 181 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Kang-Kang Wang, Lin Ju, Ya-Jun Wang, Sheng-Hong Li In this paper, our aim is to investigate the steady state characteristics and the signal-to-noise ratio (SNR) for a stochastic metapopulation system including a multiplicative periodic signal caused by the terms of the colored cross-correlated multiplicative non-Gaussian noise and additive Gaussian noise. Numerical results indicate that the multiplicative noise, the additive one and the departure parameter from the Gaussian noise can all decrease the stability of the ecological population system and restrain the development of the metapopulation, while two noise correlation times and the strength of the noise correlation will enhance the stability of the biological system and promote the expansion of the population system. With regard to the stochastic resonance phenomenon (SR) induced by noise terms and a multiplicative weak periodic signal, the results illustrate that the noise correlation time τ and the strength of correlation noise λ can increase the SR effect greatly in most cases, while the intensity of the multiplicative noise Q mainly plays a part in suppressing the SR and weakening the SNR except that in the SNR-τ plot. Moreover, it is worth noting that the noise correlation time τ 0 and the additive noise intensity M can play the diverse roles in enhancing or weakening the SR effect under the different system parameter conditions.
Authors:Sajad Jafari; Atefeh Ahmadi; Shirin Panahi; Karthikeyan Rajagopal Pages: 182 - 186 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Sajad Jafari, Atefeh Ahmadi, Shirin Panahi, Karthikeyan Rajagopal In this paper, we discuss how chaotic systems show the importance of imperfection. This happens through the butterfly effect. Then we discuss that chaotic systems with extreme multi-stability can much better demonstrate such importance. The reason is that in such systems not only the quantity of time-series is affected by butterfly effect, but also the quality of time-series is changed by small imperfections in parameters or initial conditions. We prove the importance of that difference better by comparing the efficiency of a newly proposed parameter estimation method on both an ordinary chaotic system and a chaotic system with extreme multi-stability.
Authors:Yingjuan Yang; Guoyuan Qi Pages: 187 - 195 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Yingjuan Yang, Guoyuan Qi Plasma is normally investigated via fluid dynamics, and to investigate the force and energy underlying a plasma chaotic system, it is first transformed into a Kolmogorov-type system. This system describes a general form of fluid and forced-dissipative rigid body system. The vector field of the plasma chaotic system is decomposed into four types of torque: inertial torque, internal torque, dissipation, and external torque. The Hamiltonian energy transfer between kinetic energy and potential is discovered. The various combinations of these four types of torque are constructed to uncover the effect of each on the generation of the dynamic mode of the chaotic system. The physical functions of the whistler and dampening of the pump are identified in producing the different plasma dynamics. Aside from the torque effects, the rate of change of the Casimir function is also a key factor in characterizing the orbit behavior of the plasma system. Last, a supremum bound of the plasma chaotic attractor is proposed.
Authors:Xiu-Xiu Zhan; Chuang Liu; Gui-Quan Sun; Zi-Ke Zhang Pages: 196 - 204 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Xiu-Xiu Zhan, Chuang Liu, Gui-Quan Sun, Zi-Ke Zhang Research on the interplay between the dynamics on the network and the dynamics of the network has attracted much attention in recent years. In this work, we propose an information-driven adaptive model, where disease and disease information can evolve simultaneously. For the information-driven adaptive process, susceptible (infected) individuals who have abilities to recognize the disease would break the links of their infected (susceptible) neighbors to prevent the epidemic from further spreading. Simulation results and numerical analyses based on the pairwise approach indicate that the information-driven adaptive process can not only slow down the speed of epidemic spreading, but can also diminish the epidemic prevalence at the final state significantly. In addition, the disease spreading and information diffusion pattern on the lattice as well as on a real-world network give visual representations about how the disease is trapped into an isolated field with the information-driven adaptive process. Furthermore, we perform the local bifurcation analysis on four types of dynamical regions, including healthy, a continuous dynamic behavior, bistable and endemic, to understand the evolution of the observed dynamical behaviors. This work may shed some lights on understanding how information affects human activities on responding to epidemic spreading.
Authors:Muhammad Altaf Khan; Rizwan Khan; Yasir Khan; Saeed Islam Pages: 205 - 217 Abstract: Publication date: March 2018 Source:Chaos, Solitons & Fractals, Volume 108 Author(s): Muhammad Altaf Khan, Rizwan Khan, Yasir Khan, Saeed Islam The present paper describes the dynamics of the Pine Wilt disease with variable population size. The basic mathematical results for the model are presented. The stability analysis of both the disease-free and endemic cases are presented whenever R 0 lesser or greater than one, respectively. Further, an optimal control problem is formulated and the necessarily involved results are presented. Moreover, the numerical simulation of the optimal control problem with suggested control strategies for the possible eliminations of the infection in the pine trees population is presented.
Authors:Umeshkanta Singh Thounaojam; Manish Dev Shrimali Pages: 5 - 12 Abstract: Publication date: February 2018 Source:Chaos, Solitons & Fractals, Volume 107 Author(s): Umeshkanta Singh Thounaojam, Manish Dev Shrimali In time-delay coupled relay system of three limit cycle of oscillators, linear augmentation control provides an effective strategy to induce phase-flip from relative phase zero to π between spatially separated oscillators. A coexisting dynamical regime of fixed point and anti-phase synchronization state is harnessed in relay system. Targeting phase-flip transition through linear augmentation is illustrated by using Stuart-Landau oscillators. However, such dynamical transition does not occur in the same system with conjugate coupling through dissimilar variables. Inducing relative phase difference without resorting to variation of internal system parameters and time-delay is important from the view of system control.
Authors:M. Yaqub Khan; Javed Iqbal Pages: 13 - 17 Abstract: Publication date: February 2018 Source:Chaos, Solitons & Fractals, Volume 107 Author(s): M. Yaqub Khan, Javed Iqbal Solitons and shocks formation are studied in a magnetized rotating electron-ion-positron plasma using Cairns distribution. We derive an admitted solitary wave solution KdV equation and an admitted travelling wave solution KdVB equation. We apply HPM technique on derived KdV equation and tanh-method on derived KdVB equation. It is observed that γ = T h / T P , the ratio of electron temperature to positron temperature, and α = n 0 P / n 0 h , the ratio of number density of positrons to electrons, affect both the soliton width and amplitude. It is also found that γ = T e / T P , α = n 0 P / n 0 h , kinematic viscosity and angular frequency affects the structure of shocks. We have compared our results with publish papers and conclude our results are good. This work may be helpful in order to study the rotating flows of magnetized plasma.
Authors:Akil J. Harfash; Ghazi Abed Meften Pages: 18 - 25 Abstract: Publication date: February 2018 Source:Chaos, Solitons & Fractals, Volume 107 Author(s): Akil J. Harfash, Ghazi Abed Meften We study the problem of convective movement of a reacting solute in a viscous incompressible fluid occupying a plane layer and subjected to a couple stresses effects. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. In particular, we analyse the effect of no-slip boundary conditions on the stability and instability of convection. The conditions of no-slip at the boundary with couple stresses effect and non constant coefficients which are analysed for the first time in this article.
Authors:G.P. Clemente; R. Grassi Pages: 26 - 38 Abstract: Publication date: February 2018 Source:Chaos, Solitons & Fractals, Volume 107 Author(s): G.P. Clemente, R. Grassi Several definitions of clustering coefficient for weighted networks have been proposed in literature, but less attention has been paid to both weighted and directed networks. We provide a new local clustering coefficient for this kind of networks, starting from those already existing in the literature for the weighted and undirected case. Furthermore, we extract from our coefficient four specific components, in order to separately consider different link patterns of triangles. Empirical applications on several real networks from different frameworks and with different order are provided. The performance of our coefficient is also compared with that of existing coefficients.
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