Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Ahmad Zareie, Amir Sheikhahmadi, Adel Fatemi Measurement of the spreading capability of nodes has been one of the most attractive challenges in the field of social networks. Because of the huge number of nodes in a network, it has appealed to many researchers to find an accurate measure which can potentially detect the spreading capability and rankings of nodes. Most of the available methods determine the spreading capability of nodes based on their topological locations. In this paper, however, we have proposed a new measure based on the basic notions in information theory to detect the spreading capability of nodes in networks on the basis of their topological information. The simulation and experimental results of investigating real-world and artificial networks show that the proposed measure is more accurate and efficient than the similar ones.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Yao Liu, Yashun Wang, Xun Chen, Chunhua Zhang, Yuanyuan Tan The determination of fractal dimension of rough surface profile curve is important for characterizing the fractal features of rough surface microscopic topography. There are many methods to calculate the fractal dimension, such as the power spectrum method (PSM), the structure function method (SFM), the variation method, the R/S analysis method, the wavelet transform method and etc., among which the PSM and SFM are widely used methods. This study aims to improve the computational accuracy of the fractal dimension of the profile curve. For this purpose, the two-stage method based on PSM and SFM are proposed. Firstly, we analyze the principle of calculating the fractal dimension of profile curve using PSM and SFM. Then, based on PSM and SFM, we propose a two-stage method for determining the fractal dimension of profile curve. Simulation results show that the two-stage method for fractal dimension of profile curve can greatly reduce the error compared with the original PSM and SFM. Finally, the fractal dimensions of the profile curve of the cuboid specimen are calculated by the original PSM and SFM and the two-stage method respectively. The experimental results show that the proposed method provides more precise results for determining the fractal dimension.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Peiyuan Sun, Xuesong Liu, Enze Wang, Mingfeng He, Qiuhui Pan We study the evolution of cooperation by modeling interactional individuals with compensation mechanism on a two-dimensional square lattice. In this model, the payoff to cooperators is the same no matter what types their neighbors are, while the payoff to defectors depends on whether there exists cooperative neighbor. In addition, cooperators will obtain some compensation from the payoffs of defectors. We find that a larger compensation coefficient in the model leads to the higher cooperation, which means the compensation mechanism partly promotes cooperation. In addition, the simulation results suggest that decreasing either the payoff of defectors without cooperative neighbors or the payoff of defectors with cooperative neighbors will promote cooperation.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Yahui Sun, Ling Hong, Jun Jiang The stochastic sensitivity function (SSF) method is extended to estimate the stationary probability distribution around periodic attractors of nonautonomous nonlinear dynamical systems subjected to Poisson white noise in this paper. After deriving the stochastic sensitivity functions of period-N cycle of mapping systems based on the characteristic of Poisson process, non-autonomous dynamical systems around periodic attractors are converted to mapping systems by constructing a stroboscopic map, and then the stochastic sensitivity functions of periodic attractors of nonautonomous nonlinear systems can be obtained by adopting the results of mapping systems. It is found that the stochastic sensitivity functions depend on the product of noise intensity and the arrival rate of Poisson processes. To illustrate the validity of the proposed method, a Henon map driven by Poisson processes and a Mathieu–Duffing oscillator under Poisson white noise are studied.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): B. Nana, S.B. Yamgoué, R. Tchitnga, P. Woafo The paper is devoted to theoretical and experimental investigations of an electromechanical system consisting of DC motor, a physical pendulum with the repulsive magnets. The work consists of modeling, simulation and experimental measurements to validate the analytical predictions and the numerical simulation of the earlier introduced mathematical model. The parameters of the model are estimated using the experimental data. The analyzed system shows several types of non-linear effects, including hysteresis, jump phenomena, chaos and periodic dynamics. Good agreement between real and simulated behavior of the system is obtained.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Chen Chu, Jinzhuo Liu, Chen Shen, Jiahua Jin, Yunxuan Tang, Lei Shi Evolutionary prisoner's dilemma game in structured populations on a weighted square lattice, on which the edge weight represents the relationship between agents and adaptively changes in time, has been proved to be an efficient way that can promote cooperation. In fact, such an adaptive link weight introduces a new time scale τa , not necessarily equal to the time scale of game strategy τ ɛ. Inspired from aforementioned above, we investigate the effect of w = τ ɛ τ a on the evolution of cooperative behavior. Through numerical simulation, we find cooperation can be promoted effectively with a larger value of w, which is related to the increase of average link weight in the structured population.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Dawei Ding, Jie Yan, Nian Wang, Dong Liang This paper investigates the synchronization of fractional order complex-variable dynamical networks with time-varying coupling. Based on information of the complex network's configuration, an effective adaptive pinning control strategy to adjust simultaneously coupling strength and feedback gain is designed. Besides, we also consider the synchronization in complex networks with time-varying coupling weight. By constructing suitable Lyapunov function and using the presented lemma, some sufficient criteria are derived to achieve the synchronization of fractional order complex-variable dynamical networks under the corresponding update law. The update law is only dependent on the states of the complex dynamical networks, which do not need any other information such as the characteristic of the uncoupled nodes of the networks. Further, the result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field. Finally, the correctness and feasibility of the proposed theoretical results are verified by two examples of fractional complex-variable dynamic networks.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Qiu Li, MingChu Li, Lin Lv, Cheng Guo, Kun Lu Infectious diseases have proven to be remarkably resilient foes of human health and so the prevention and control of infectious diseases have been attracting the attention of all countries over the world. Vaccination is an effective way to prevent the spread of infectious diseases. However, vaccination is a long-standing social dilemmas due to the vaccine’s risk by itself and the spread of infectious diseases in the population depends on not only the pathogen itself, but also the impact of social network structures. In this paper, we propose a new prediction model of infectious diseases with new vaccination strategies based on network structures and dynamic replicator. In our model, we consider not only the subsidies of vaccine failure but also the incentive strategy for medical treatment to promote individuals to take the initiative to vaccinate. At the same time, in decision-making phase, we use weighted average benefits of all participants to update their strategies due to individual difference. Simulation experiments show that the our proposed model is much effective and better than other existing models. We also use Jacobian matrix to prove the stability of dynamic equilibrium for our proposed model.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Enrique de Amo, Manuel Díaz Carrillo, Juan Fernández-Sánchez We introduce and study representation systems for the numbers in the unit interval [0, 1]. We call them ϕm -systems (where ϕm is a pseudo-golden ratio). With the aid of these representation systems, we define a family hm of strong negations and an increasing function gm which is the inverse of the generator of hm . The functions hm and gm are singular, and we study several properties; among which we calculate the Hausdorff dimensions of certain sets that are related to them. Finally, we prove that gm is an infinite convolution, and the sequence of coefficients in the Fourier series of its associated Stieltjes measure does not converge to zero.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): A. Ahmadian, S. Salahshour, M. Ali-Akbari, F. Ismail, D. Baleanu This paper focuses on providing a new scheme to find the fuzzy approximate solution of fractional differential equations (FDEs) under uncertainty. The Caputo-type derivative base on the generalized Hukuhara differentiability is approximated by a linearization formula to reduce the corresponding uncertain FDE to an ODE under fuzzy concept. This new approach may positively affect on the computational cost and easily apply for the other types of uncertain fractional-order differential equation. The performed numerical simulations verify the proficiency of the presented scheme.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Xingpeng Zhang, Dong Li, Xiaohong Zhang Randomness is a common phenomenon in nonlinear systems. And conditions to reach synchronization are more complex and difficult when chaotic systems have random parameters. So in this paper, an adaptive scheme for synchronization of chaotic system with random parameters by using the fuzzy impulsive method and combining the properties of Wiener process and Ito differential is investigated. The main concepts of this paper are applying fuzzy method to approximate the nonlinear part of system, then using Ito differential to study the Wiener process of random parameters of chaotic system, and realizing synchronization under fuzzy impulsive method. The stability is analyzed by Lyapunov stability theorem. At the end of the paper, numerical simulation is presented to illustrate the effectiveness of the results obtained in this paper.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Ali Durdu, Yılmaz Uyaroğlu In this study, a novel three dimensional autonomous chaotic attractor was found and secure communication masking application was performed with optimal fractional order, which offers more precise and faster results than first order chaotic equations, via Pecaro Carroll synchronization algorithm. The shortest synchronization time was investigated with optimal fractional order value. In the novel secure communication synchronization application with fractional order chaotic system, there is an angle of 45° between the signals sent and received, which clearly shows that the system can be employed in secure communication.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): R. Sahadevan, P. Prakash Lie symmetry analysis and invariant subspace methods of differential equations play an important role separately in the study of fractional partial differential equations. The former method helps to derive point symmetries, symmetry algebra and admissible exact solution, while the later one determines admissible invariant subspace as well as to derive exact solution of fractional partial differential equations. In this article, a comparison between Lie symmetry analysis and invariant subspace methods is presented towards deriving exact solution of the following coupled time fractional partial differential equations: (i) system of fractional diffusion equation, (ii) system of fractional KdV type equation, (iii) system of fractional Whitham-Broer-Kaup’s type equation, (iv) system of fractional Boussinesq-Burgers equation and (v) system of fractional generalized Hirota-Satsuma KdV equation.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Weiping Wang, Minghui Yu, Xiong Luo, Linlin Liu, Manman Yuan, Wenbing Zhao In this paper, the global asymptotic stability of memristive bidirectional associative memory neural networks with leakage delay and two additive time-varying delays is firstly studied. Then, we propose a novel sampled-data feedback controller to guarantee the synchronization of system based on drive/response concept. In particular, taking full advantage of the input delay approach, the Lyapunov function method and the Jensen’s inequality theory, several sufficient conditions are obtained. Finally, two numerical simulation examples show the effectiveness of the designed sampled-data control strategy. Furthermore, our results can be applied to simulate the associative memory function of brain-like robots, large-scale information storage, etc.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Gabriel Gajardo, Werner Kristjanpoller We apply MF-ADCCA to analyze the presence and asymmetry of the cross-correlations between Latin-American and US stock market indices and crude oil market. We find that multifractality exists in this cross-correlations, and that there is asymmetry on its behavior. The asymmetry degree changes accordingly to the series considered for the trend behavior. We find that fluctuation sizes greatly influence the asymmetry in the cross-correlation exponent, increasing for large fluctuations when we consider the trend of the crude oil price. We also find no clear differences in the exponents with different scales under different trends of the WTI, contrary to other studies in asymmetric scaling behavior. When we examine the time varying features of the asymmetry degree we find that the US indices show a consistent behavior in time for both trends, where the cross-correlation exponents tend to be larger for downward trends. On the other hand, given the more heterogeneous individual properties of Latin-American indices, the asymmetry behavior varies more depending on the trend considered.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Chris G. Antonopoulos, Charalampos Skokos, Tassos Bountis, Sergej Flach In the study of subdiffusive wave-packet spreading in disordered Klein–Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG particle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q − Gaussian probability distribution functions of sums of position observables with q > 1 always approach pure Gaussians ( q = 1 ) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonicity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this system in the subdiffusive energy domain using q-statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t = 10 9 .

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Viktor Avrutin, Jose D. Morcillo, Zhanybai T. Zhusubaliyev, Fabiola Angulo Power electronic DC/AC converters (inverters) play an important role in modern power engineering for a broad variety of applications including solar and wind energy systems as well as electric and hybrid cars drives. It is well known that the waveform of the output voltage (or current) of an inverter may be significantly distorted by phase restricted high frequency oscillations, frequently referred to as bubbling. However, the reasons leading to the appearance of this undesired effect are still not completely understood. Considering as an example a 2D model of a PWM H-bridge single-phase inverter, the present paper reports the appearance of two different kinds of bubbling. In the first case, the appearance of bubbling occurs suddenly and is related to the change of periodicity. We show that high-periodic, quasiperiodic and chaotic oscillations may exhibit bubbling, and also that solutions with and without bubbling may coexist. In the second case, the appearance of bubbling occurs gradually in the parameter domain where the investigated system undergoes border collisions of so-called persistence type. As a result, the appearance of the bubbling of the second kind does not change the periodicity of the motion but nevertheless disturbs the waveform. We discuss some differences in the properties of the second kind of bubbling from the first one, and present numerical techniques for its detection.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): I.A. Shepelev, D.V. Shamshin, G.I. Strelkova, T.E. Vadivasova We study the boundaries of existence of traveling waves and stationary spatial structures in an active medium model by varying the control parameters. The medium is represented by a ring of diffusively coupled FitzHugh–Nagumo neurons, which, when uncoupled, can demonstrate excitable, self-sustained oscillatory or bistable dynamics depending on control parameter values. The dynamical regimes realized in the medium are compared with those ones observed in an individual FitzHugh–Nagumo neuron. Possible bifurcations of traveling waves are analyzed when the dynamics of the medium elements changes. We also explore the influence of the relaxation level of FitzHugh–Nagumo neurons on the medium dynamics.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Can Li, Zun-Guang Guo, Zhi-Yu Zhang Brucellosis is a major problem worldwide in public health and existing work mainly focused on severity estimation based on the real data. However, global analysis on brucellosis transmission model is not well understood. In this paper, we presented a dynamical model of brucellosis transmission coupled with sheep and human populations and global analysis is shown based on Lyapunov functions. We found that the global dynamics of brucellosis model is determined by basic reproduction number R 0: if R 0 < 1, then the disease-free equilibrium is globally asymptotically stable; otherwise, the endemic equilibrium is globally asymptotically stable. We hope that our study may provide theoretical basis for the further work on brucellosis control.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Debajyoti Saha, Pankaj Kumar Shaw, Sabuj Ghosh, M.S. Janaki, A.N.S. Iyengar The evidence of finite nonlinear interaction in a DC glow discharge plasma has been demonstrated by estimating phase coherence index for different types external forcing techniques likewise noise, sinusoidal, square etc. The existence of finite phase coherence index i.e finite correlation prompts us to carry out nonlinearity analysis using delay vector variance (DVV). Finite nonlinear interaction obtained from phase coherence index values is observed to be predominant at a particular amplitude of square forcing which corroborates our nonlinearity analysis using DVV. Existence of phase coherence index has been demonstrated introducing continuous wavelet transform (CWT). Characterization of the difference in the phase distribution by the difference in the waveform in real space instead of dealing in Fourier space has been facilitated by introducing structure function or path length for different orders to study and identify the dynamical system. The expression of path length eventually enables us to evaluate the phase coherence index. The transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Peng Gang Sun, Xiaoke Ma, Juan Chi By identifying important nodes (driver nodes), the minimum dominating set (MDS) provides an effective model to dominate complex networks. However, in many networks, the skeleton of driver nodes selected using the MDS is usually connected, which motivates us to explore a new framework and try to dominate a network by identifying its minimum skeleton. We define the minimum skeleton of a graph as a subgraph induced from the nodes within the minimum connected dominating set (MCDS), and the problem can be solved by a maximum spanning tree-based algorithm. For the domination of complex networks, in general, the MCDS needs more driver nodes, and is more robust than the MDS against link attack. Interestingly, for the MDS, it is harder to control the networks with weaker communities, while for the MCDS, this finding tends to be observed on the networks with homogeneous community sizes. In addition, for the MDS, the curves for the percentage of driver nodes on the networks with variable community strengths shift downward as the average degree of the networks increases, while for the MCDS, the curves, like power functions rotate clockwise. For the both, it tends to be harder to control the networks with stronger overlapping, and the number of driver nodes is dependent on the networks’ degree distribution.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Fengji Peng, Wen Wang, Shengyou Wen We prove that, given 0 ≤ β ≤ α and α ≤ λ ≤ β + α , there exist compact subsets X, Y of the Euclidean space R ⌈ α ⌉ such that dim A X = α , dim A Y = β and dim A ( X × Y ) = λ , where ⌈α⌉ is the smallest integer ≥ α and dim A denotes Assouad dimension. In the proof an Assouad dimension formula for uniform Cantor sets is established.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Kálmán Klapcsik, Ferenc Hegedűs In this study, a nonlinear investigation of a periodically driven gas bubble in glycerine is presented. The bifurcation structure of the bubble oscillator (Keller–Miksis equation) is explored in the pressure amplitude-frequency parameter plane of the excitation by means of initial (high resolution bi-parametric plots) and boundary value problem solvers at various ambient temperatures. The range of the applied temperature covers two orders of magnitude difference in the liquid viscosity which is the main damping factor of the system. Therefore, the evolution of the harmonic and ultraharmonic resonances are presented starting with an overdamped behaviour (there are no resonances in the parameter space) and ending up with a fully developed bifurcation superstructure. The results reveal a complex period bubbling mechanism organized in a Farey-tree; inside each bubble a fine substructure of alternating chaotic and periodic bands exist. The description of the bifurcation structure presented throughout the paper can help to understand the mechanism of dissipation on the behaviour of nonlinear systems in more detail.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Jiaquan Zhang, Dan Lu, Shunkun Yang Epidemic spreading has been intensively studied in SIS epidemic model. Although the mean-field theory of SIS model has been widely used in the research, there is a lack of comparative results between different theoretical calculations, and the differences between them should be systematically explained. In this paper, we have compared different theoretical solutions for mean-field theory and explained the underlying reason. We first describe the differences between different equations for mean-field theory in different networks. The results show that the difference between mean-field reaction equations is due to the different probability consideration for the infection process. This finding will help us to design better theoretical solutions for epidemic models.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): D. Youmbi Fouego, E.D. Dongmo, P. Woafo This work deals with the analysis of the voltage amplitude generated in a linear load by an array of Van der Pol (VDP) and Hindmarsh–Rose (HR) oscillators. For the array of Van der Pol oscillators, it is found that after a threshold number of oscillators under which the power is equal to zero, the power increases with the size of the array. A high order nonlinearity in the damping of the Van der Pol oscillator increases the power. In the case of the array of HR oscillators, it is shown that varying the coupling coefficient leads to the appearance of chaotic dynamics in the system. Contrary to the case of the VDP oscillators, it is found that the voltage amplitudes decrease when the size of the array of the HR oscillators increases. These results can be linked to the mechanism of biological oscillators powering biological organs.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Vladimir A. Maximenko, Alexander E. Hramov, Alexey A. Koronovskii, Vladimir V. Makarov, Dmitry E. Postnov, Alexander G. Balanov The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Marcel Ausloos, Roy Cerqueti, Tariq A. Mir This paper explores a real-world fundamental theme under a data science perspective. It specifically discusses whether fraud or manipulation can be observed in and from municipality income tax size distributions, through their aggregation from citizen fiscal reports. The study case pertains to official data obtained from the Italian Ministry of Economics and Finance over the period 2007–2011. All Italian (20) regions are considered. The considered data science approach concretizes in the adoption of the Benford first digit law as quantitative tool. Marked disparities are found, - for several regions, leading to unexpected “conclusions”. The most eye browsing regions are not the expected ones according to classical imagination about Italy financial shadow matters.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Xue-feng Zhang, Feng-bao Yang, Xu-zhu Wang In 1982, Dubois and Prade investigated the relationship between belief function, plausibility function and basic probability assignment when the involved universe is finite. In this paper, the similar results on their relationships are obtained with a continuous universe. As an important facility to connect possibility distribution in continuous universes and discrete probability values, basic probability histogram is defined by means of measurement amplitude, which is a notion with both probability and possibility features. A theorem about how to calculate a suitable sample size for estimation is proposed based on the researches on basic probability histograms. Through the theorem, we can directly calculate the appropriate samples size for any population distribution. Even with small samples, a reasonable estimation can be obtained with a non-normal distribution.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Jian-Qin Qiao, Li Li As we all known, there are many kinds of strains for a disease. However, the transmission dynamics of such disease is far from being well understood. In this paper, we established a SIS multi-strain model on scale-free network and the dynamics of multi-strain disease was studied by mean-field method. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R 0 < 1. It is proved that the equilibrium point with the largest basic reproduction number is globally stable. Our results indicate that competitive exclusion principle also holds for the disease with multiple strains.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Liguo Fei, Yong Deng How to identify influential nodes is still an open and vital issue in complex networks. To address this problem, a lot of centrality measures have been developed, however, only single measure is focused on by the existing studies, which has its own shortcomings. In this paper, a novel method is proposed to identify influential nodes using relative entropy and TOPSIS method, which combines the advantages of existing centrality measures. Because information flow spreads in different ways in different networks. In the specific network, the appropriate centrality measures should be considered to sort the nodes. In addition, the remoteness between the alternative and the positive/negetive ideal solution is redefined based on relative entropy, which is proven to be more effective in TOPSIS method. To demonstrate the effectiveness of the proposed method, four real networks are selected to conduct several experiments for identifying influential nodes, and the advantages of the method can be illustrated based on the experimental results.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Hui Zhao, Lixiang Li, Jinghua Xiao, Yixian Yang, Mingwen Zheng In this paper, a class of periodically switch control method is proposed to achieve finite-time parameters tracking identification and synchronization for multi-link complex networks. This periodically switch control is an optimal control, two convertible control intensities are given in a fixed period instead of continuous high control intensity. Meanwhile, we give an effective analysis for complex network model with multiple constant time-delays and time-varying delays, we overcome these difficulties of time-delays and unknown parameters. The parameters estimation, topological identification are achieved based on parameters tracking identification of drive-response networks. Meanwhile, the corresponding identification and synchronization criteria are obtained based on Lyapunov function, linear matrix inequality (LMI) and finite-time stability theory. Finally, numerical simulations are given to verify the effectiveness of our proposed method.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Li Liu, Xiaofeng Luo, Lili Chang Pair approximation model is an effective tool to study epidemic spread on complex networks. It can more accurately capture the effects of network structure on the spreading process. That then helps us grasp the spreading laws of epidemics on networks and further make effective prevention and control measures. Vaccination, an important measure for prevention and control of infectious disease, has made great achievements in public health. In this paper we study vaccination strategies with the help of pair approximation epidemic model with demographics. We firstly introduce constant vaccination into SIR pair approximation model. The reproduction number and endemic prevalence of disease are investigated, the critical vaccination rate which can help to control disease transmission is also given. Considering the restriction of financial resources, it is necessary to control disease transmission simultaneously to reduce vaccination cost. To this end, we further investigate optimal vaccination of SIR pair approximation model by use of optimal control theory. The existence of optimal solution is established and optimality system is derived. Finally, a series of stochastic simulations on different initial networks are performed to demonstrate our theoretical models and some numerical simulations are provided to observe and analyze different vaccination strategies.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): Zhenghong Deng, Chunmiao Ma, Xudong Mao, Shenglan Wang, Zhenxi Niu, Li Gao Understanding the evolution of cooperation among selfish individuals remains a large challenge. Network reciprocity has been proved to be an efficient way that can promote cooperation and has spawned many studies focused on network. Traditional evolutionary games on graph assumes players updating their strategies based on their current payoff, however, historical payoff may also play an indispensable role in agent's decision making processes. Another unavoidable fact in real word is that not all players can know exactly their historical payoff. Based on these considerations, in this paper, we introduce historical payoff and use a tunable parameter u to control the agent's fitness between her current payoff and historical payoff. When u equals to zero, it goes back to the traditional version; while positive u incorporates historical payoff. Besides, considering the limited knowledge of individuals, the structured population is divided into two types. Players of type A, whose proportion is v, calculate their fitness using historical and current payoff. And for players of type B, whose proportion is 1 − v , their fitness is merely determined by their current payoff due to the limited knowledge. Besides, the proportion of these types keeps unchanged during the simulations. Through numerous simulations, we find that historical payoff can promote cooperation. When the contribution of historical payoff to the fitness is larger, the facilitating effect becomes more striking. Moreover, the larger the proportion of players of type A, the more obvious this promoting effect seems.

Abstract: Publication date: November 2017 Source:Chaos, Solitons & Fractals, Volume 104 Author(s): S. Behnia, M. Yahyavi, R. Habibpourbisafar Hierarchy of one-dimensional ergodic chaotic maps with Tsallis type of q-deformation are studied. We find that in the chaotic region, these maps with q-deformation are ergodic as the Birkhoff ergodic theorem predicts. q-deformed maps are defined as ratios of polynomials of degree N. Hence, by using the Stieltjes transform approach (STA), invariant measure is proposed. In addition, considering Sinai-Ruelle-Bowen (SRB) measure, Kolmogorov-Sinai (KS) entropy for q-deformed maps is calculated analytically. The new q-deformed scheme have ability to keep previous significant properties such as ergodicity, sensitivity to initial condition. By adding q-parameter to the hierarchy in order increase the randomness and one-way computation, we present a new scheme for watermarking. The introduced algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security. To illustrate the effectiveness of the proposed scheme, some security analyses are presented. By considering the obtained results, it can be concluded that, this scheme have a high potential to be adopted for watermarking. It can be concluded that, the proposed novel watermarking scheme for image authentication can be applied for practical applications.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Zhuoqun Li, Shiwei Sun, Yongchun Huang Considering the non-negative constraint of order quantity, this study explored inventory system performance, including system stability, service level, inventory cost, and the effect of transportation delay time. Both the non-negative constraint and delay time render the system nonlinear and complicated, which makes it difficult to identify optimal order policy regions that combine system stability with a high service level and low cost. The purpose of this study is to systematically reflect the impact of order policies on inventory system performance from three aspects, including system stability, service level, and cost. The results of the simulation revealed the existence of public optimal order policies for different transportation delay times. Although these optimal order policies are similar when the target inventory parameter changes, lowering the target inventory parameter can also lower the inventory cost. If an appropriate order policy can be adopted, a low target inventory reduces inventory cost while maintaining system stability and a high service level, opening up new options for decision makers in supply chain management.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Lina Song From the point of view of fractional calculus and fractional differential equation, the work handles European option pricing problems with transaction costs in fractal market. Under the definition of the modified Riemman-Liouville fractional derivative, the pricing model based on a space-time fractional patrial differential equation is presented by the replicating portfolio, containing the Hurst exponent taken as the order of fractional derivative. And then, European call and put options are constructed and calculated by the enhanced technique of Adomian decomposition method under the finite difference frame. The fractional derivative model is finally tested by the data from the option market.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Harendra Singh, H.M. Srivastava, Devendra Kumar The key purpose of this article is to introduce a numerical algorithm for the solution of the fractional vibration equation (FVE). The numerical algorithm is based on the applications of the operational matrices of the Legendre scaling functions. The main advantage of the numerical algorithm is that it reduces the FVE into Sylvester form of algebraic equations which significantly simplify the problem. Error as well as convergence analysis of the proposed scheme are shown. Numerical results are discussed taking different initial conditions and wave velocities involved in the problem. Numerical results obtained by using suggested numerical algorithm are compared with the existing analytical methods for the different cases of FVE.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Saravanan M., Emmanuel Yomba We study the nonlinear dynamics of the electromagnetic wave propagation in a spin-torque driven helimagnet which accounts for the fundamental magnetic interactions. The dynamical Landau–Lifshitz equation includes the magnetic spin exchange, anisotropy, helimagnetic spin coupling through the anti-symmetric Dzyaloshinskii–Moriya interaction driven by the applied electric current density. The electromagnetic wave propagation is governed by the Maxwell equation with the induced current density factor. On the basis of the reductive perturbation method, we present a higher order nonlinear Schrödinger (NLS) equation as a reduction of the Maxwell–Landau model. Through the direct ansatz method, we derive a set of solutions for the NLS equation. These solutions include bright, dark and kink or front soliton solutions for certain specific conditions imposed on the spin-torque helimagnet.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Marius-F. Danca, Nikolay Kuznetsov In this paper we unveil the existence of hidden chaotic sets in a simplified Hopfield neural network with three neurons. It is shown that beside two stable cycles, the system presents hidden chaotic attractors and also hidden chaotic transients which, after a relatively long life-time, fall into regular motions along the stable cycles.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Shuang Liu, Hongling Ai, Zhenjun Lin, Zong Meng The dynamic equation of some nonlinear torsional vibration system with two masses is established, which contains backlash. In the case of primary resonance, the frequency response equation of the system is deduced with the modified Lindstedt–Poincare method combined with the multiple scales method. The influence of the backlash change on the amplitude of the torsional vibration system is analyzed by the amplitude frequency response map, and by using the method of numerical analysis, the influence of the backlash change on the system entering the chaotic motion is analyzed by bifurcation diagram, the maximum Lyapunov exponent map, phase diagram and Poincare map. After adding the method of the adaptive continuous perturbation control, the amplitude of the system decreases, and there is a transformation from chaotic motion to periodic motion.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Oussaeif Taki-Eddine, Bouziani Abdelfatah In this paper, we establish sufficient conditions for the existence and uniqueness of the solution in functional weighted Sobolev space for a class of initial-boundary value problems with integral condition for a class of nonlinear partial fractional reaction-diffusion (RD) equations. The results are established by using a priori estimate in Bouziani fractional spaces and applying an iterative process based on results obtained for the linear problem, we prove the existence, uniqueness of the weak generalized solution of the nonlinear problem.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Dharmbir Prasad, Aparajita Mukherjee, V. Mukherjee In this paper, a real parameter metaheuristic optimization algorithm (named as chaotic krill herd algorithm (KHA) (CKHA)) is analyzed to solve optimal power flow (OPF) based DC link placement problem. The present study appears to be well capable for replacement of the existing transmission lines by direct current (DC) links to have more secured, flexible and economical operation. DC link equations are incorporated into the conventional OPF problem for the solution of this type of problem. The IEEE 30-bus and IEEE 57-bus test power systems are used to demonstrate the performance of the proposed CKHA. The simulation results obtained from both KHA and CKHA techniques are compared to other recent evolutionary optimization techniques surfaced in the recent state-of-the-art literature. It is revealed that the proposed approach secures better consequence over the other newly originated popular optimization techniques (including basic KHA) and reflects its improved quality solutions and faster convergence speed.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Tian Bian, Yong Deng In the field of complex networks, how to identify influential nodes in complex networks is still an open research topic. In the existing evidential centrality (EVC), the global structure information in complex networks is not taken into consideration. In addition, EVC also has the limitation that only can be applied on weighted networks. In this paper, a New Evidential Centrality (NEC) is proposed by modifying the Basic Probability Assignment (BPA) strength generated by EVC. According to the shortest paths between the nodes in the network rather than just considering local information, some other BPAs are constructed. With a modified combination rule of Dempster–Shafer evidence theory, the new centrality measure is determined. Numerical examples are used to illustrate the efficiency of the proposed method.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Najmeddine Attia, Bilel Selmi, Chouhaïd Souissi In this paper, we establish some density results related to the multifractal generalization of the centered Hausdorff and packing measures. We also focus on the exact dimensions of locally finite and Borel regular measures. We, then, apply these theories to a class of Moran sets satisfying the strong separation condition.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): O. Foupouapouognigni, C. Nono Dueyou Buckjohn, M. Siewe Siewe, C. Tchawoua In this paper, an electromechanical energy harvesting system exhibiting the fractional properties and subjected to the harmonic excitation is investigated. The main objective of this paper is to discuss the system performance with parametric coupling and fractional derivative. The dynamic of the system is presented, plotting bifurcation diagram, poincaré map, power spectral density and phase portrait. These results are confirmed by using 0 − 1 test. The harmonic balance method is used with the goal to provide the analytical response of the electromechanical system. The numerical simulation validates the results obtained by this analytical technique. In addition, replacing the harmonic by the random excitation, the impact of noise intensity, the fractional order derivatives κ and the amplitude of the parametric coupling γ is investigated in detail. It points out from these results that for the best choice of D, κ and γ, the output power can be improved.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Nandadulal Bairagi, Debadatta Adak Clinical studies show intra-patient variability of real time data of host cells and virus particles in case of HIV infection. However, basic HIV models do not show oscillations unless self-proliferation of host cells is considered. Extended basic models with immune response also do not show oscillations unless delay is considered. In this study we investigate whether oscillations can be the result of immune response alone in a more realistic model in absence of delay and without self-proliferation of host cells. For this purpose, we study the interaction of host cells, virus specific T-lymphocytes and human immunodeficiency virus with generalized infection rate and sigmoidal function for CTL expansion in presence and absence of self-proliferation of helper cells. Stability and instability of both systems are determined with respect to the parameter that measures the virus replication. It is shown that an otherwise stable interior equilibrium of the system without or with self-proliferation may be unstable and show oscillations in presence of immune response. More specifically, the interior equilibrium of both systems may switch its stability more than once in presence of immune response. Our analysis indicates that immune response alone may be responsible for producing oscillations and thus exhibit intra-patient variability of host cells and virus particles in vivo non-delayed HIV models in presence or absence of self-proliferation of host cells.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Zhiwen Chen, Xin Wang, Shouming Zhong, Jun Yang This paper studies the problem of delay-dependent passivity for uncertain neural networks (UNNs) with discrete and distributed delays. Without considering free weighting matrices and multiple integral terms, which may cause more numbers of linear matrix inequalities (LMIs) and scalar decision variables. By constructing a suitable Lyapunov–Krasovskii functional (LKF) and combining with the reciprocally convex approach, some sufficient conditions are established in terms of LMIs. Compared with existing results, the derived criteria are more effective due to the application of delay partitioning approach which takes a full consideration of all available information in various delay intervals. Two simulation examples are given to illustrate the effectiveness of the proposed method.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Santu Ghorai, Swarup Poria In this paper, diffusion driven pattern forming instabilities in a predator-prey system with mutually interfering predators described by the Beddington-DeAngelis type functional response, are investigated in the presence of additional food for predators. Conditions for Hopf, Turing and wave instabilities are investigate around the coexisting equilibrium point analytically. Numerical simulation results are presented to show different types of spot, stripe and their mixture patterns. Different spatial domains in the parameter space are plotted. The existence and non-existence of positive, non-constant, steady states of the reaction-diffusion model are established. It is observed that spatio-temporal pattern of a predator prey system can change significantly depending upon the parameters related to additional food. We can conclude from our study, that the reasons of appearance of different spatio-temporal patterns in the real life ecological systems may be due to variation of additional food.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Wakil Sarfaraz, Anotida Madzvamuse This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary rectangular domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter space is fully classified in terms of the types and stability of the uniform steady state. In the absence of diffusion the results on the classification of parameter space are supported by simulations of the corresponding vector-field and some trajectories of the phase-plane around the uniform steady state. In the presence of diffusion, the main findings are the quantitative analysis relating the domain-size with the reaction and diffusion rates and their corresponding influence on the dynamics of the reaction-diffusion system when perturbed in the neighbourhood of the uniform steady state. Theoretical predictions are supported by numerical simulations both in the presence as well as in the absence of diffusion. Conditions on the domain size with respect to the diffusion and reaction rates are related to the types of diffusion-driven instabilities namely Turing, Hopf and Transcritical types of bifurcations. The first condition is a lower bound on the area of a rectangular domain in terms of the diffusion and reaction rates, which is necessary for Hopf and Transcritical bifurcation to occur. The second condition is an upper bound on the area of domain in terms of reaction-diffusion rates that restricts the diffusion-driven instability to Turing type behaviour, whilst forbidding the existence of Hopf and Transcritical bifurcation. Theoretical findings are verified by the finite element solution of the coupled system on a two dimensional rectangular domain.