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): Md. Nasim Akhtar, M. Guru Prem Prasad, M.A. Navascués The box dimension of the graph of non-affine α-fractal interpolation function fα with variable scaling factors is estimated in the interval [0, 1]. Due to the non-affinity of fα , the behavior of the graph is non-uniform in the subintervals. An attempt is made to estimate the box dimension of the graph of fα in the subintervals as well and it is compared with the box dimension of fα on the whole interval.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): K.P. Harikrishnan, R. Misra, G. Ambika In the context of chaotic dynamical systems with exponential divergence of nearby trajectories in phase space, hyperchaos is defined as a state where there is divergence or stretching in at least two directions during the evolution of the system. Hence the detection and characterization of a hyperchaotic attractor is usually done using the spectrum of Lyapunov Exponents (LEs) that measure this rate of divergence along each direction. Though hyperchaos arise in different dynamical situations and find several practical applications, a proper understanding of the geometric structure of a hyperchaotic attractor still remains an unsolved problem. In this paper, we present strong numerical evidence to suggest that the geometric structure of a hyperchaotic attractor can be characterized using a multifractal spectrum with two superimposed components. In other words, apart from developing an extra positive LE, there is also a structural change as a chaotic attractor makes a transition to the hyperchaotic phase and the attractor changes from a simple multifractal to a dual multifractal, equivalent to two inter-mingled multifractals. We argue that a cross-over behavior in the scaling region for computing the correlation dimension is a manifestation of such a structure. In order to support this claim, we present an illustrative example of a synthetically generated set of points in the unit interval (a Cantor set with a variable iteration scheme) displaying dual multifractal spectrum. Our results are also used to develop a general scheme to generate both hyperchaotic as well as high dimensional chaotic attractors by coupling two low dimensional chaotic attractors and tuning a time scale parameter.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Jian Pan, Qingxian Xiao This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the expected utility maximization framework, where the stochastic interest rate follows the Hull-White interest rate model and the inflation risk is modelled by an additional stochastic process. The investor can invest in n + 1 assets: cash, a default-free zero-coupon bond, an inflation-indexed bond and n − 2 stocks. The liability process is given by a geometric Brownian motion rather than a Brownian motion to ensure a definite liability value. Applying the stochastic control theory and partial differential equation approach, we obtain the explicit solutions of optimal investment strategies for the power utility and exponential utility functions. We also provide numerical examples to show the effects of model parameters on the optimal investment strategies.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Yanfei Jin, Zhengmu Ma, Shaomin Xiao In this paper, the dynamical analysis of a periodic potential subject to noise without and with the periodic signal is presented. The third-order differential equation of the stationary probability density (SPD) is derived for the periodic potential, which driven by multiplicative dichotomous and additive white noise. It is found that the SPD undergoes a transition from the unimodal to the bimodal structure with the increase of multiplicative noise intensity. The power spectra density (PSD) and the qualify factor show the peak structure when a suitable dose of noise intensity is added. That is, the coherence resonance (CR) appears. Meanwhile, the average input energy per period and the amplitude of average response are calculated to quantify stochastic resonance (SR). The curve of the average input energy per period shows multiple extrema as a function of multiplicative noise intensity at the small fixed additive noise intensity. This phenomenon indicates the stochastic multi-resonance happens for this case.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Karthikeyan Rajagopal, Akif Akgul, Sajad Jafari, Anitha Karthikeyan, Ismail Koyuncu There are many recent investigations on chaotic systems with self-excited and hidden attractors. In this paper we introduce a chaotic system in which the attractor can change between hidden and self-excited attractor depending on the value of parameters. Dynamical properties of the proposed attractor are investigated. The attractor is then realized using off the shelf components. Also, for this new system electronic circuit is implemented and FPGA-based chaotic oscillator is designed. In the end, the fractional- order form is examined through bifurcation and stability analysis.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Karthikeyan Rajagopal, Anitha Karthikeyan, Ashokkumar Srinivasan A novel chaotic memfractor oscillator with one unstable equilibriums is proposed. Various dynamic properties of the proposed system are derived and investigated to show the existence of chaotic oscillations. The fractional order time delayed model of the chaotic memfractor oscillator is derived considering time delay in the memcapacitor. Bifurcation of the time delayed system with its delay factor is investigated along with the parameter space bifurcation. A novel methodology for synchronizing identical time delayed systems with an uncertainty in the slave system is proposed and tested with the proposed time delayed fractional order chaotic memfractor oscillator.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Hong-Li Li, Cheng Hu, Haijun Jiang, Zhidong Teng, Yao-Lin Jiang This paper investigates the synchronization problem of general complex networks with fractional-order dynamical nodes. Pinning state feedback controllers have been proved to be effective for synchronization control of fractional-order complex networks. We will show that pinning intermittent controllers are also effective for synchronization control of general fractional-order complex networks. Based on the Lyapunov method and periodically intermittent control method, several low-dimensional criteria are derived for the synchronization of such dynamical networks. Finally, a numerical example is presented to demonstrate the validity and feasibility of the theoretical results.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Kyunghyun Park, Junkee Jeon In this paper, we derive an analytic formula for the American knock-out options with rebate. Rather than using a probabilistic method, we use the Laplace–Carson Transform(LCT) method to induce a simple functional equation associated with the complex problem of option pricing Partial Differential equation with free boundary. The transformed value of free boundary could be solved by applying Newton’s method. Lastly, numerical Laplace inversion techniques are used to solve for the wanted free boundary value and the options value.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Kyunghyun Park, Myungjoo Kang, Yong Hyun Shin This paper attempts to choose the optimal consumption, leisure, investment, and voluntary retirement time under the negative wealth constraint. The Dynamic Programming method is used to derive the value function and to identify the optimal policies when the agent’s utility function of consumption and leisure is given in the form of Cobb–Douglas. Finally, the effects of negative wealth constraints were discussed by examining the optimal policies that vary depending on the degree of the negative wealth constraint.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): C.J. Zúñiga-Aguilar, H.M. Romero-Ugalde, J.F. Gómez-Aguilar, R.F. Escobar-Jiménez, M. Valtierra-Rodríguez In this paper, we approximate the solution of fractional differential equations using a new approach of artificial neural network. We consider fractional differential equations of variable-order with Mittag-Leffler kernel in Liouville–Caputo sense. With this new neural network approach, it is obtained an approximate solution of the fractional differential equation and this solution is optimized using the Levenberg–Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional differential equations, the Willamowski-Rössler oscillator and a multi-scroll system. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network different performance indices were calculated.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): K.R. Raslan, Khalid K. Ali, Muhannad A. Shallal In this paper, we established a traveling wave solution by using the modified extended tanh method for space-time fractional nonlinear partial differential equations. The method is used to obtain exact solutions for different types of space-time fractional nonlinear partial differential equations such as space-time fractional equal width wave equation (EWE) and space-time fractional modified equal width wave equation (MEW) which are important soliton equations. Both equations are reduced to ordinary differential equations by using fractional complex transform and properties of modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Paolo Grigolini This is a call for papers that should contribute to the unification of behavioral sciences and team management, focusing on the biological origin of cooperation and swarm intelligence, moving from biology to psychology and from sociology to political science, with the help of the theoretical tools of complex networks. This issue should shed light into the origin of ergodicity breaking and contribute to establishing a connection, still lacking theoretical support, between complexity properties that are expected to be correlated. Examples are: non-Poisson renewal events and multi-fractality; complexity matching and chaos synchronization; criticality and extended criticality of small size systems. Although the emphasis is on systems of small size, and especially on the search of the size maximizing both information transport and cooperation emergence, special attention will be devoted to the interaction between small groups and their larger societies.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Rana D. Parshad, Aladeen Basheer, Debaldev Jana, Jai Prakash Tripathi Predator interference, or a decline in the per predator consumption rate as predator density increases, is generally considered a stabilizing mechanism in two-species predator-prey models. There is significant debate, as to whether prey handling predators, might interfere in the hunting process of prey searching predators, or whether these are mutually exclusive events. In the current manuscript, a three species food chain model, with strong top predator interference is considered. We prove that in terms of explosive instability/finite time blow up, sufficient interference by prey handling predators always tends to destabilize the system. The dynamics of a time delayed version, as well as the spatially explicit model are also explored. We use our results to comment on a certain paradox in ecological theory, as well as provide further insight into the nature of predator interference, and exploding populations of invasive species.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Ram Jiwari, Sukhveer Singh, Ajay Kumar This work deals to capture the different types of patterns of nonlinear time dependent coupled reaction-diffusion models. To accomplish this work, a new differential quadrature (DQ) algorithm is developed with the help of modified trigonometric cubic B-spline functions. The stability part of the developed algorithm is studied by matrix stability analysis method. In the experimental part, different types of patterns of Gray–Scott, Schnakenberg, Isothermal Chemical and Brusselator Models are captured which are similar to the existing patterns of the models.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Shang Gao, Songsong Li, Boying Wu In this paper, we consider the existence of periodic solutions for discrete time periodic time-varying coupled systems on networks (DPTCSN). Some novel sufficient conditions are obtained to guarantee the existence of periodic solutions for DPTCSN, which have a close relation to the topology property of the corresponding network. Our approach is based on the continuation theorem of coincidence degree theory, generalized Kirchhoff’s matrix tree theorem in graph theory, Lyapunov method and some new analysis techniques. The approach is applied to the existence of periodic solutions for discrete time Cohen–Grossberg Neural Networks (CGNN). Finally, an example and numerical simulations are provided to illustrate the effectiveness of our theoretical results.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Soodabeh Lashgarinezhad, Amir Hossein Sari, Davoud Dorranian Effects of nonthermal electrons and positrons on the nature of ion acoustic cnoidal wave in the plasma contains ions, positrons, and electrons are investigated. Reductive perturbation method was employed to solve the fluid dynamic equations with appropriate boundary condition and derivation of Korteweg-de Vries (KdV) equation for nonlinear periodic ion acoustic wave. Sagdeev potential was extracted and the condition of plasma nonthermality on the formation of solitary and cnoidal ion acoustic wave has been discussed in detail. Results show that for all magnitudes of electrons (positrons) nonthermal coefficient, α e (α p) ion acoustic wave may generate in plasma medium. With increasing both α e and α p the amplitude of cnoidal ion acoustic wave increases. The wavelength of ion acoustic wave increases with increasing α p and decreases with increasing α e.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): M.A. Menouer, A. Moussaoui, E.H. Ait Dads A periodic predator-prey model has been introduced in [5] to study the effect of water level on persistence or extinction of fish populations living in an artificial lake. By using the continuation theorem of Mawhin’s coincidence degree theory, the authors give sufficient conditions for the existence of at least one positive periodic solution. In this paper we study the problem in the general case. We begin by analyzing the invariance, permanence, non-persistence and the globally asymptotic stability for the system. Most interestingly, under additional conditions, we find that the periodic solution obtained in [5] is unique. Finally, in order to make the model system more realistic, we consider the special case when the periodicity in [5] is replaced by almost periodicity. We obtain conditions for existence, uniqueness and stability of a positive almost periodic solution. The methods used in this paper will be comparison theorems and Lyapunov functions. An example is employed to illustrate our result.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): A. Bakhshalizadeh, R. Asheghi, R. Hoseyni In this paper, we study the Chebyshev’s property of the three-dimensional vector space E = < J 0 , J 1 , J 2 > , where J i ( h ) = ∫ H = h x i d x y and H ( x , y ) = 1 2 y 2 + V ( x ) is a hyperelliptic Hamiltonian of degree 7. Our main result asserts that in two specific cases, namely (a) V ′ ( x ) = x 3 ( x − 4 7 ) ( x − 1 ) 2 and (b) V ′ ( x ) = x ( x − 2 7 ) ( x − 1 ) 4 , E is an extended complete Chebyshev system. To this end, we use the criterion and the tools developed by Grau–Mañosas–Villadelprat in Trans. Amer. Math. Soc. in 2011.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Yu’e Wu, Bin Zhang, Shuhua Zhang Reward and punishment are crucial for the emergence and sustainability of cooperation in evolutionary games. In this work, we introduce a third-party agent, who plays the role of a judge to reward cooperators and punish defectors, to study the impact of reward and punishment on the evolution of cooperation. The introduced righteous agent is different from the cooperators and defectors in the traditional games and it exists as a judge independent of the processes of the games. In each round of the evolutionary game, each player has a half chance to confront the righteous agent. If the player is a cooperator, it’s possible for it to obtain an extra profit. On the contrary, when a defector meets the righteous agent, its earnings may be reduced. The simulation results show that the introduction of the righteous agent in the evolutionary game favors the evolution of cooperation. The robustness of the promoting effect is tested for different complex topologies for the prisoner’s dilemma game. The enhancement effects are confirmed in the snowdrift game as well, which may imply that the facilitation effects show a high degree of universality independent of the structure of the applied spatial networks and the potential evolutionary game models. Our conclusion may be conducive to interpret the emergence and sustainability of cooperation within the structured populations.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Hamid Niknazar, Ali Motie Nasrabadi, Mohammad Bagher Shamsollahi This paper presents a methodology to extract a number of quantifier features to characterize volumetric behavior of trajectories in phase space. These features quantify expanding and contracting behaviors and complexity that can be used in nonlinear and chaotic signals classification or clustering problems. One of the features is directly extracted from the distance matrix and seven features are extracted from a matrix that is subsequently obtained from the distance matrix. To illustrate the proposed quantifiers, Mackey–Glass time series and Lorenz system were employed and feature evaluation was performed. It is shown that the proposed quantifier features are robust to different initializations and can quantify volumetric behavior characteristics. In addition, the ability of these features to differentiate between signals with different parameters is compared with some common nonlinear features such as fractal dimensions and recurrence quantification analysis features.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Marcelo A. Savi, Francisco Heitor I. Pereira-Pinto, Flavio M. Viola, Aline Souza de Paula, Davide Bernardini, Grzegorz Litak, Giuseppe Rega Shape Memory Alloy (SMA) dynamical systems may exhibit a rich response that can include periodic, quasi-periodic, chaotic and hyperchaotic behaviors. In this regard, diagnostic tools are important in order to identify the different types of behaviors. This paper aims to analyze systems with SMA elements through a nonlinear dynamics perspective with a specific focus on the use of 0–1 test to quantify the chaoticity of the dynamical response of SMA oscillators. The investigation includes different constitutive models for the restitution force on both single- and two-degree of freedom oscillators. Results of the 0–1 test are compared with Lyapunov exponents calculated with different algorithms. The analyses show that the 0–1 test can be considered a reliable and computationally efficient alternative as a diagnostic tool of chaotic responses.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Amr Elsonbaty, A.A. Elsadany The aim of this work is to conduct analytical bifurcation study for exploring the possible varieties of bifurcations and dynamics exist in a new deterministic chaotic system, which models reversals of the Earth magnetic field. First, the basic dynamical properties of the system are analyzed by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Second, the parameters’ regions for supercritical and subcritical Andronov–Hopf bifurcations along with the dynamics associated with the codimension two Horozov–Takens bifurcation are studied. Then, the homoclinic bifurcation of the system is analytically investigated. Results reveal that the presence of coexistent attractors in the phase space of the model is possible where they take the forms of equilibria or periodic orbits. Also, it is observed that the existence of homoclinic bifurcation is a key factor that leads to the more complex behaviors and chaos. Finally, numerical simulations are carried out to validate and confirm the results.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Salim Lahmiri, Gazi Salah Uddin, Stelios Bekiros We attempt to quantify the intrinsic nonlinear dynamics of thirty international financial markets. Fractality, chaoticity and randomness are explored during and after the recent global financial crisis. We find that most markets exhibited persistent long-range correlations during the crisis, whilst anti-persistent patterns are identified after the crisis. Moreover, the nonlinear dynamics in all markets do not exhibit chaotic features. Importantly, the degree of randomness has increased in most of markets in the aftermath of the crisis. Overall, the nonlinear characteristics of the temporal dynamics of the major financial markets have been notably modified in the post-crisis period.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Farman Ullah, Sungchang Lee Online social networking websites provide platforms through which users can express opinions and preferences on a multitude of items and topics, and follow users and information, and flood it by retweeting. User-user interests vary, and based on the users’ interests, they can be grouped to multiple implicit interest communities. However, every interaction and user may not be trustworthy. Capturing the user's interaction with others, and predicting user interest and trust from the interactions are important parts of social media analytics. In this paper, we propose community clustering for implicit community detection based on trust and interest modeling. The trust modeling is weighted by the user's interests to group the users in multiple clusters having higher interest and trust similarity within a cluster. The proposed community clustering algorithm begins by ranking the nodes by the weighted degree and then selecting the initial community centers that are not in the neighbors of each other's. We then assign the user to the community with whom the user has the higher interest and trust similarity and higher common connections topology. We provide a probabilistic trust model to predict the unknown reliable trust between users considering their friends. We model user interests based on preferences and opinions, as well as the content experienced in social media. Furthermore, we evaluate the proposed algorithm comparing publicly available datasets with well-known algorithms for clustering quality.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): S. Morfu, M. Bordet In this paper, we first report the response of an elementary FitzHugh–Nagumo electronic circuit excited by a low frequency sine wave and perturbed by an additive high frequency deterministic perturbation. This preliminary study constitutes a reference to analyze the collective behavior of a chain of 45 coupled elementary cells. In particular, we focus on the propagation of a low frequency sine wave which is only applied on the first fifteen cells of the lattice. It is shown that a high frequency sine wave which perturbs the whole network can enable or disable the propagation of this low frequency signal. By reducing the strength of the intercellular coupling below a critical value, we also establish that the propagation fails whatever the amplitude of the perturbation. Finally, by adding a stochastic perturbation to the high frequency deterministic perturbation, we numerically and experimentally investigate their combined effects on the propagation of the low frequency component. Numerical and experimental results reveal that, under certain conditions, noise can assist the propagation of the low frequency excitation.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Yan Liu, Tong Chen, Yongjie Wang Many scholars have devoted to study how to improve the level of cooperation and amount of mechanisms have been presented. However, what makes cooperation sustainable' Village Opera is a kind of public cultural activities in southern China and has been on until now. It is a good example that cooperation can maintain a long time and the pattern of Village Opera is similar to public goods game(PGG). So we investigate Village Opera by PGG. To better understand the process of evolution in Village Opera, we introduce three types of agents into our spatial PGG. Through numerical simulations, we find We find that reputation can promote cooperation and reputation is influenced by habitual preference(β). Moreover, the key is that demand or tradition can maintain the cooperation level when reputation is disappear in Village Opera.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Li Zhang, Fangqi Chen Analytic and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Stability parametric regions and multiple bifurcations for the system are investigated. The damping coefficients of the plunge and pitch are considered as perturbation parameters. With aid of center manifold and normal form theories, the stability regions of the initial equilibrium point and the explicit expressions of the critical bifurcation curves are achieved, which can result in static bifurcation and Hopf bifurcation. Nonlinear flutter happens with a phenomenon of limit cycle oscillations (LCOs) when the damping coefficients are less than or greater than the linear critical values. Under certain conditions, quasi-periodic motions on 2T torus may occur. These complex dynamical behaviours are discussed in detail in this paper. This is useful to characterize the effects of different parameters on structural nonlinearities of the system and ensure that aerodynamic flutter of the airfoil does not take place. Finally, the numerical solutions simulated by four-order Runge–Kutta method are illustrated to tally with the analytic results.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): S. Sabari, K. Porsezian, P. Muruganandam Analyzing a Gross–Pitaevskii equation with cubic, quartic, and quintic nonlinearities through analytical and numerical methods, we examine the stability of two-dimensional (2D) trapless Bose–Einstein condensates (BECs) with two-, three-body interactions and quantum fluctuations. Applying a variational approach, we derive the equation of motion and effective potential to discuss in detail the stability of the BECs in 2D free space. We show that with the aid of quantum fluctuations it is possible to stabilize 2D trapless BEC without any oscillatory nonlinearities. Also, there is an enhancement of the stability of the system, due to the inclusion of the three-body interaction and quantum fluctuations in addition to the two-body interaction. We further study the stability of 2D trapless BECs with rapid periodic temporal modulation of scattering length by using a Feshbach resonance. We discuss all possible ways of stabilization of trapless BECs in 2D by three-body interaction and quantum fluctuations. Finally, we verify our analytical results with numerical simulation using split-step Crank–Nicholson method. These match well with the analytical predictions.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Zhen Wang, Yamir Moreno, Stefano Boccaletti, Matjaž Perc This is an introduction to the special issue titled “Vaccination and epidemics in networked populations” that is in the making at Chaos, Solitons & Fractals . While vaccination is undoubtedly one of the most important preventive measures of modern times, epidemics are feared as one of the most damaging phenomena in human societies. Recent research has explored the pivotal implications of individual behavior and heterogeneous contact patterns in networked populations, as well as the many feedback loops that exist between vaccinating behavior and disease propagation [1, 2]. Interdisciplinary explorations in the realm of statistical physics, network science, nonlinear dynamics, and data analysis have given rise to theoretical epidemiology, as well as to the theory of epidemic processes in complex networks. From classical models assuming well-mixed populations and ignoring human behavior, to recent models that account for behavioral feedback and population structure, we have come a long way in understanding disease transmission and disease dynamics, and in using this knowledge to devise effective prevention strategies. This special issue is aimed at helping the further development of these synergies. We hope that it contributes to enhance our understanding of vaccination and epidemics in networked populations, by featuring works related to vaccination and epidemics using techniques ranging from complex and temporal networks to network of networks and show-casing the possibilities of interdisciplinarity via complex systems science to tackle the challenges in our quest for a healthier future. Topics of interest include but are not limited to epidemiological modeling and vaccination, behavior-vaccination dynamics, reaction-diffusion processes and metapopulation models, evolutionary and game theoretical models in epidemiology, as well as to influence maximization and digital epidemiology.

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): Jun Tanimoto Network reciprocity is one of the key mechanisms to solve social dilemmas, and has attracted many researchers for the last decade. Here, we explore what happens if network reciprocity is dovetailed with indirect reciprocity. This is motivated by the idea that a player may utilize observed information to evaluate his neighbors. Simulations based on our minimal model reveal that adding indirect reciprocity does not always increase the level of cooperation beyond the level of model without indirect reciprocity. This implies that the combination of two different reciprocity mechanisms, each enhancing cooperation if applied independently, can lead negative interference effect on cooperation. The details of this depend on type of action assessment system determining what is good and bad. Interestingly, we found that a high level of information is not always superior to low levels of information.

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): Han-Xin Yang, Lijun Tian We propose a conformity-driven reproductive ability in which an individual i is more (less) likely to imitate a neighbor j’s strategy if j’s strategy is majority (minority) in i’s neighborhood. The results on the evolutionary spatial prisoner’s dilemma game show that, compared to homogeneous reproductive ability, conformity-driven reproductive ability can greatly enhance cooperation. This finding is robust with respect to different types of network structures (including square lattice and scale-free network) and to different ways of strategy updating (including synchronous and asynchronous strategy updating).

Abstract: Publication date: October 2017 Source:Chaos, Solitons & Fractals, Volume 103 Author(s): J.S. Cánovas, M. Muñoz-Guillermo In this paper we compute topological entropy with prescribed accuracy for different economic models, showing the existence of a topologically chaotic regime for them. In order to make the paper self-contained, a general overview on the topological entropy of continuous interval maps is given. More precisely, we focus on piecewise monotone maps which often appear as dynamical models in economy, but also in population growth and physics. Our main aim is to show that when topological entropy can be approximated up to a given error, it is a useful tool which helps to analyze the chaotic dynamics in one dimensional models.

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.