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

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

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

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

Abstract: Publication date: Available online 10 March 2017 Source:Chaos, Solitons & Fractals Author(s): C. Burgos, J.-C. Cortés, L. Villafuerte, R.-J. Villanueva This paper extends both the deterministic fractional Riemann–Liouville integral and the Caputo fractional derivative to the random framework using the mean square random calculus. Characterizations and sufficient conditions to guarantee the existence of both fractional random operators are given. Assuming mild conditions on the random input parameters (initial condition, forcing term and diffusion coefficient), the solution of the general random fractional linear differential equation, whose fractional order of the derivative is α ∈ [0, 1], is constructed. The approach is based on a mean square chain rule, recently established, together with the random Fröbenius method. Closed formulae to construct reliable approximations for the mean and the covariance of the solution stochastic process are also given. Several examples illustrating the theoretical results are included.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Mohd. Junaid Siddiqui, Rajan Arora, Anoop Kumar The propagation of plane and cylindrical shock waves in a perfectly conducting ideal gas in presence of transverse magnetic field is studied for a point explosion. The density ahead of the shock front is assumed to vary as a power of the distance from the source of explosion. The plasma is assumed to be an ideal gas with infinite electrical conductivity permeated by a transverse magnetic field. Following Sakurai [1, 2], the first approximate exact solutions are obtained by expanding the variables in the form of power series in (C/U)2, where C is the speed of sound in undisturbed medium of the flow. Numerical description of the flow field has been presented in an ideal magnetogasdynamics. The results obtained are compared with the numerical solutions obtained by Sakurai in the absence of magnetic field. Also, the effect of magnetic field on flow variables such as density, velocity, pressure and magnetic pressure behind the wave front is illustrated through figures. It is very interesting in particular that exact analytical solutions are obtained for this problem.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Samia M. Said, Yassmin D. Elmaklizi, Mohamed I.A. Othman In the present paper, we introduced a general model of the equations of the formulation in the context of Lord–Shulman theory which includes one thermal relaxation time and Green–Lindsay theory with two thermal relaxation times as well as the classical dynamical coupled theory to study the effect of the rotation and the magnetic field on the total deformation of a micropolar thermoelastic medium with an internal heat source that is moving with a constant speed. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. Comparisons made with the results of the three theories in the presence and absence of the magnetic field as well as an internal heat source. A comparison is also made with the results of the three theories for different values of the rotation.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Ai-Zhong Shen, Jin-Li Guo, Qi Suo This paper presents the influence of two kinds of variable growth hypernetworks on the scaling law of hypernetworks. Our model can be degenerated to the original evolving model. On one hand, we establish the variable growth of hyperedges evolving hypernetworks model and obtain the stationary average hyperdegree distribution of the model by employing the Poisson process theory and the continuous method. The theoretical analyses in this paper agree with the conducted numerical simulations. The results show that the transient average hyperdegree distribution of the hypernetwork follows the scale-free law. However, the stationary average hyperdegree distribution does not, which indicates that the number of hyperedges at each time step affects the scaling law of hypernetworks. On the other hand, we establish the new nodes variable growth hypernetworks model and obtain analytical solutions of the transient average hyperdegree distribution. We simulate to compare the different node growth rate effect on the hyperdegree distribution characteristics. The results show that the growth rate does not affect the scaling law properties of the hypernetworks. Only when λ = 1 can we obtain analytical solutions of stationary average hyperdegree distribution of the hypernetwork which is not scale-free law.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Jiaojiao Yang, Antti Käenmäki, Min Wu Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Valeria Bondarenko, Victor Bondarenko, Kyryl Truskovskyi We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The method of checking the adequacy of the proposed model is developed and short-term forecasting for temporary data is constructed. The research results are implemented in software tools for analysis and modeling of time series.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): M. Messadi, A. Mellit This paper concerns the control problems of an induction motor with chaotic behavior due to the defiance of indirect field oriented control applied with a proportional integral (PI) speed loop. The feedbacks predictive control is used to control this chaotic system owing to its simplicity of configuration and implementation. In general, the gain of the predictive control used in the literature is taken as a constant included in an interval, however, in this work, this gain is taken a matrix and Linear matrix inequality is using to calculate this gain. To highlight the efficiency and applicability of the proposed control scheme, simulations and experimental results are presented.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Jeong-Hoon Kim, Chang-Rae Park The pricing of financial derivatives based on stochastic volatility models has been a popular subject in computational finance. Although exact or approximate closed form formulas of the prices of many options under stochastic volatility have been obtained so that the option prices can be easily computed, such formulas for exchange options leave much to be desired. In this paper, we consider two different risky assets with two different scales of mean-reversion rate of volatility and use asymptotic analysis to extend the classical Margrabe formula, which corresponds to a geometric Brownian motion model, and obtain a pricing formula under a stochastic volatility. The resultant formula can be computed easily, simply by taking derivatives of the Margrabe price itself. Based on the formula, we show how the stochastic volatility corrects the Margrabe price behavior depending on the moneyness and the correlation coefficient between the two asset prices.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Saeed Farzami Sarcheshmeh, Reza Esmaelzadeh, Mehdi Afshari In this paper, two master and slave chaotic satellites will be synchronized acceptably using two different control methods. The first method is based on the neural networks in which two neural controllers called NARMA-L2 and Predictive controllers will be designed. In the second method a Nonlinear controller is designed by the Feedback linearization approach. The simulation results of the designed controllers have been compared with a performed control method called Active control to verify the effectiveness of the proposed controllers and to show the advantages and disadvantages of each one.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Minhyuk Lee, Jae Wook Song, Ji Hwan Park, Woojin Chang We detect the asymmetric multi-fractality in the U.S. stock indices based on the asymmetric multi-fractal detrended fluctuation analysis (A-MFDFA). Instead using the conventional return-based approach, we propose the index-based model of A-MFDFA where the trend based on the evolution of stock index rather than stock price return plays a role for evaluating the asymmetric scaling behaviors. The results show that the multi-fractal behaviors of the U.S. stock indices are asymmetric and the index-based model detects the asymmetric multi-fractality better than return-based model. We also discuss the source of multi-fractality and its asymmetry and observe that the multi-fractal asymmetry in the U.S. stock indices has a time-varying feature where the degree of multi-fractality and asymmetry increase during the financial crisis.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Yeyin Xu, Albert C J Luo, Zhaobo Chen In this paper, analytical solutions of periodic motions in a 1-D nonlinear dynamical system are obtained through the generalized harmonic balance method with prescribed-computational accuracy. From this method, the 1-D dynamical system is transformed to a nonlinear dynamical system of coefficients in the Fourier series. The analytical solutions of periodic motions are obtained by equilibriums of the coefficient dynamical systems, and the corresponding stability and bifurcations of periodic motions are completed via the eigenvalue analysis. The frequency-amplitude characteristics of periodic motions are analyzed through the different-order harmonic terms in the Fourier series, and the corresponding quantity levels of harmonic amplitudes are determined. From such frequency-amplitude characteristics, the nonlinearity, singularity and complexity of periodic motions in the 1-D nonlinear systems can be discussed. Displacements and trajectories of periodic motions are illustrated for a better understanding of periodic motions in the 1-D nonlinear dynamical systems. From this study, the periodic motions in the 1-dimensional dynamical systems possess similar behaviors of periodic motions in the van der Pol oscillator.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Sarika Jalan, Alok Yadav, Camellia Sarkar, Stefano Boccaletti The fractal nature of graphs has traditionally been investigated by using the network’s nodes as the basic units. Here, instead, we propose to concentrate on the graph’s edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.

Abstract: Publication date: April 2017 Source:Chaos, Solitons & Fractals, Volume 97 Author(s): Monik Borghezan, Paulo C. Rech We investigate a two-dimensional parameter-space of a three-parameter, three-variable, continuous-time dynamical system, namely the Vallis model for El Niño phenomenon. We report on modifications in this parameter-space, as a function of the third parameter which is varied. More specifically we report on organization of chaos and periodicity, showing the existence of periodic structures embedded in a chaotic region, which are organized in period-adding sequences.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Prem Kumar Singh Recently, the calculus of concept lattice is extended from unipolar to bipolar fuzzy space for precise measurement of vagueness in the attributes based on their acceptation and rejection part. These extensions still unable to highlight the uncertainty in vague attributes and measurement of fluctuation at given phase of time. To conquer this problem, current paper proposed a method for adequate analysis of vagueness and uncertainty in data with fuzzy attributes using the amplitude and phase term of a defined complex vague set based concept lattice. In addition, the analysis derived from the proposed method is compared with CVSS method through an illustrative example.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): K. Karamanos, I.S. Mistakidis, S.I. Mistakidis The correlation function of the trajectory exactly at the Feigenbaum point of the logistic map is investigated and checked by numerical experiments. Taking advantage of recent closed analytical results on the symbol-to-symbol correlation function of the generating partition, we are in position to justify the deep algorithmic structure of the correlation function apart from numerical constants. A generalization is given for arbitrary m · 2∞ Feigenbaum attractors.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): A.S. Elwakil, A. Agambayev, A. Allagui, K.N. Salama The purpose of this work is to provide an experimental demonstration for the development of sinusoidal oscillations in a fractional-order Hartley-like oscillator. Solid-state fractional-order electric double-layer capacitors were first fabricated using graphene-percolated P(VDF-TrFE-CFE) composite structure, and then characterized by using electrochemical impedance spectroscopy. The devices exhibit the fractional orders of 0.6 and 0.74 respectively (using the model Z c = R s + 1 / ( j ω ) α C α ), with the corresponding pseudocapacitances of approximately 93nF sec − 0.4 and 1.5nF sec − 0.26 over the frequency range 200kHz–6MHz (Rs < 15Ω). Then, we verified using these fractional-order devices integrated in a Hartley-like circuit that the fractional-order oscillatory behaviors are of orders 2.6 and 2.74.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Jiahua Jin, Chen Shen, Chen Chu, Lei Shi In spatial evolutionary games, the fitness of each player is usually measured by its inheritance (i.e. the accumulated payoffs by playing the game with its all nearest neighbors), or by the linear combination of its inheritance and its environment (i.e. the average of its all nearest neighbors’ inheritance). However, a rational individual incorporates environment into its fitness to develop itself only when environment is dominant in real life. Here, we redefine the individual fitness as a linear combination of inheritance and environment when environment performs better than inheritance. Multiple Monte Carlo simulation results show that incorporating dominant environment can improve cooperation comparing with the traditional case, and furthermore increasing the proportion of prevailing environment can enhance cooperative level better. These findings indicate that our mechanism enhances the individual ability to adapt environment, and makes the spatial reciprocity more efficient. Besides, we also verify its robustness against different game models and various topology structures.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): M. Saleh, N. Alkoumi, Aseel Farhat In this paper, we will investigate the dynamics of a nonlinear rational difference equation of a higher order. Our concentration is on invariant intervals, periodic character, the character of semi-cycles and global asymptotic stability of all positive solutions of x n + 1 = α + β x n + γ x n − k B x n + C x n − k , n = 0 , 1 , … It is worth to mention that our results solve partially some of the open problems proposed by Kulenvic and Ladas in their monographs [17], [18].

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): B.G. Sidharth, Abhishek Das In this paper, we endeavor to extend the noncommutative relations between the coordinates and the momenta. We find that the momentum operators conform to anti-commutation rules. This helps us to explain the extra terms emerging in case of the Landau quantization and we find that the emerging magnetic term is a direct consequence of the noncommutative nature of space-time. This intuition has been further extended to explain the large magnetic fields arising from compact stellar bodies.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Renji Han, Binxiang Dai A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Joydev Ghosh, Banshidhar Sahoo, Swarup Poria The impacts of additional food for predator on the dynamics of a prey-predator model with prey refuge are investigated. The equilibrium points and their stability behaviours are determined. Hopf bifurcation conditions are derived analytically. Most significantly, existence conditions for unique stable limit cycle in the phase plane are shown analytically. The analytical results are in well agreement with the numerical simulation results. Effects of variation of refuge level as well as the variation of quality and quantity of additional food on the dynamics are reported with the help of bifurcation diagrams. It is found that high quality and high quantity of additional food supports oscillatory coexistence of species. It is observed that predator extinction possibility in high prey refuge ecological systems may be removed by supplying additional food to predator population. The reported theoretical results may be useful to conservation biologist for species conservation in real world ecological systems.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Chun Zhang, Liping Du, Tonghuan Wang, Tao Yang, Chunhua Zeng, Canjun Wang In this paper, stationary probability distribution (SPD), mean first passage time (MFPT) and stochastic resonance (SR) phenomenon of an abstract model of the Myc/E2F/MiR-17-92 network with time delay and cross-correlation noise sources are investigated. The impacts of time delay τ, additive and multiplicative noise intensities Q and D, and cross-correlation intensity λ between noises on the SPD, MFPT, and SNR are discussed, respectively. Research results show that: (i) the high protein level (or ON) state is enhanced (or weaken) by the τ (or λ); (ii) the MFPT as a function of Q or D exhibits a maximum, which is the signature of the noise enhanced stability (NES) of the ON state. The stability of the ON state can also enhance (or weaken) by the λ (or τ); (iii) the existence of a maximum and a minimum in the signal-to-noise ratio (SNR) is identifying the characteristics of the SR and stochastic reverse-resonance (SRR) phenomenon, τ and λ enhance the SR and weaken the SRR phenomenon for SNR as a function of Q, while τ (or λ) weakens (or enhances) the SR phenomenon for SNR as a function of D; and (iv) the time delay weakens the SR, and causes the SR phenomenon to disappear for SNR as a function of λ.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Jaume Giné, Jaume Llibre We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Alper Korkmaz The bright soliton solutions and singular solutions are constructed for the space-time fractional EW and the space-time fractional modified EW (MEW) equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform (FCT) and properties of modified Riemann–Liouville derivative. Then, various ansatz method are implemented to construct the solutions for both equations.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Changjin Xu, Peiluan Li This paper is concerned with a class of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee that all solutions of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays converge exponentially to zero vector are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Somenath Mukherjee, Rajdeep Ray, Rajkumar Samanta, Mofazzal H. Khondekar, Goutam Sanyal The natural complexity of wireless mobile network traffic dynamics has been assessed in this article by tracing the presence of nonlinearity and chaos in the profile of daily peak hour call arrival and daily call drop of a sub-urban local mobile switching centre. The tools like Recurrence Plot and Recurrence Quantification Analysis (RQA) has been used to reveal the probable presence of non-stationarity, nonlinearity and chaosity in the network traffic. Information Entropy (IE) and 0–1 test have been employed to provide the quantitative support to the findings. Both the daily peak hour call arrival profile and the daily call drop profile exhibit non-stationarity, determinism and nonlinearity with the former one being more regular while the later one is chaotic.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Qingchu Wu, Shufang Chen, Lingling Zha We discuss the impact of local information-based behavioral response on epidemic spreading in social networks. By using a pair quenched mean-field approach developed by Mata and Ferreira [Europhys. Lett. 103 (2013) 48003], we derive a dynamical model governing the epidemic spreading over a random network with a linear response function and density-dependent epidemic information. A deterministic relation between the epidemic threshold and the response parameter is derived according to a quasi-static approximation method. It is found that local behavioral response will induce the extinction of the disease via rasing the epidemic threshold. Additionally, the theoretical result is supported by stochastic simulations on an Erd o ¨ s–Rényi random network and a Barab a ´ si–Albert scale-free network. Simulations show that the pair quenched mean-field approach is more accurate than the classical quenched mean-field approach.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Charikleia Gkarlaouni, Stanislaw Lasocki, Eleftheria Papadimitriou, Tsaklidis George Temporal and spatial analysis of seismicity is performed via the Rescaled Range (R/S) analysis for revealing the hidden characteristics of long memory dependence and clustering between earthquakes. The analysis is applied in two seismogenic units belonging to the extensional Aegean back-arc region, namely the Corinth rift and the Mygdonian graben. The Hurst exponent estimations were used for the interpretation of earthquake collective properties, regarding magnitude, interevent time and interevent epicentral distance for consecutive events. Additional stochastic tools were then engaged for the validation of the results. Τhe analysis outcome is a significant long memory content in the seismic process of both areas, especially for the interevent time of recent micro seismicity and moderate earthquakes in the last decades. This property is not ascertained for the strong (M ≥6.0) historical earthquakes indicating that stronger events are rather independent, whereas the weaker ones may be primary carriers of persistence in the seismogenesis process.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Canshi Zhu, Xiaoyang Wang, Lin Zhu In order to evaluate the influence of nodes in complex networks, a new method is advanced of evaluating key nodes in complex networks, in combination with the “structural hole” theory and closeness centrality of nodes, through defining and applying the influence matrix of nodes’ “structural holes” in response to the limitations of existing methods. The “structural hole” theory gives a comprehensive consideration of the node degree as well as information about topological relations with its neighbors, whereas the closeness centrality of nodes is a reflection of the node's global information. The “structural holes” influence matrix in degree reflects the node's local and global information. So a more proper evaluation standard is established for influence of nodes and a simulation analysis is made of different-scale networks. The results of such analyses show that the method can not only make an exact assessment of the influence of nodes, but also obtain ideal evaluation results from actual complex networks of different scale.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Vivek Sharma, B.B. Sharma, R. Nath In the present manuscript, observer based synchronization and message recovery scheme is discussed for a system with uncertainties. LMI conditions are analytically derived solution of which gives the observer design matrices. Earlier approaches have used adaptive laws to address the uncertainties, however in present work, decoupling approach is used to make observer robust against uncertainties. The methodology requires upper bounds on nonlinearity and the message signal and estimates for these bounds are generated adaptively. Thus no information about the nature of nonlinearity and associated Lipschitz constant is needed in proposed approach. Message signal is recovered using equivalent output injection which is a low pass filtered equivalent of the discontinuous effort required to maintain the sliding motion. Finally, the efficacy of proposed Nonlinear Unknown Input Sliding Mode Observer (NUISMO) for chaotic communication is verified by conducting simulation studies on two chaotic systems i.e. third order Chua circuit and Rossler system.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Caiping Xi, Shuning Zhang, Gang Xiong, Huichang Zhao, Yonghong Yang There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Xiang Shao, Rongliang Lu, Cao Zhao In this paper, we give the multifractal analysis of the weighted local entropies for arbitrary invariant measures. Our result is applied to self-affine systems.

Abstract: Publication date: March 2017 Source:Chaos, Solitons & Fractals, Volume 96 Author(s): Francesca Di Patti, Duccio Fanelli, Filippo Miele, Timoteo Carletti The Complex Ginzburg–Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ultimately responsible for the onset of a generalized class of topological instability, reminiscent of the Benjamin–Feir type. The analysis is initially carried out for a specific class of networks, characterized by a circulant adjacency matrix. This allows us to delineate analytically the domain in the parameter space for which the generalized instability occurs. We then move forward to considering the family of non linear oscillators coupled via a generic direct, though balanced, graph. The characteristics of the emerging patterns are discussed within a self-consistent theoretical framework.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Yael Scharf Biological systems such as the cell are mostly analyzed by looking at the biophysical properties of their inner workers, such as proteins. However, some have suggested that biological systems have quantum properties in addition to their physical complexities. Thus, these systems can be measured by the displacement and geometry or the velocity of the acting agents inside them. In this paper I suggest that measurement of displacement or of biophysical properties does not suffice when calculating the dynamics of the system, and vice versa. Furthermore, I propose a theoretical background to approach and measure the dynamics of biological systems by using the chaos theory as means of calculation. This approach will be exemplified in evolution, development and cancer with a strong emphasis on endosymbiosis of the mitochondria and the cell in genetic aspects.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Hongzhe Dai, Zhibao Zheng, Wei Wang In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): M.M. El-Nahass, A.A. Attia, H.A.M. Ali, G.F. Salem, M.I. Ismail ZnIn2Se4 thin films were deposited on glass substrates by thermal evaporation technique. Some of ZnIn2Se4 films were annealed under vacuum at 623K for 2h. Atomic force microscope (AFM) images were analyzed for as-deposited and annealed films. The roughness degree of the film surface decreased under the influence of annealing. DC Electrical conductivity studied as a function of temperature. Two activation energies were determined that ΔE 1 = 0.44eV and ΔE 2 = 0.65eV. Using thermo-electric measurements, the thermoelectric power factor (P), carrier concentration (n) and mobility (μ) were calculated. Current density–voltage characteristics of Al/ZnIn2Se4/Al sandwich structure were examined. Different mechanisms were obtained; ohmic conduction mechanism at lower voltages and space charge limited conductivity (SCLC) mechanisms at higher voltages.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): A. Pourdarvish, J. Sadeghi, N.J. Hassan In this paper, we derive the non Markovian master equation (NMME) that correspond to position non Markovian stochastic Schrödinger equation (PNMSSE) in linear and non linear cases. In this case, using Nivokov property we derive four formulas of (NMME) for linear and non linear cases respectively. The functional derivative operator may depend on time and independent with respect to noise. Here, we determine the functional derivative of statistical operator. When the functional derivative operator depends on time and noise, one can calculate the perturbation and post Markovian perturbation for the functional operator, which exists in position non Markovian equation of motion (PNMEM). In order to explain our theory, we present a simple non Markovian example. Finally, we give the conclusion and the plan for future works.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Bing Hu, Shun Chen, Hongmei Chi, Jin Chen, Peipei Yuan, Huihui Lai, Wangyuan Dong In this paper, we use a basal ganglia-corticothalamic model (BGCT) to study control effect of the absence epilepsy seizure. It is shown that the seizure state can be well controlled by tuning activation level of the thalamic reticular nucleus (TRN), specific relay nuclei (SRN), striatal D1 neurons and striatal D2 neurons. And then, one type of deep brain stimulation voltage employed on SRN, we find that seizure activities can also be controlled by tuning the period (P) and the duration of effective current (D) in a period into some appropriate ranges. So, we infer that the thalamic and striatal tissue may become effective target regions in clinical treatment of epilepsy in the future.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Tetsushi Ohdaira Regarding costly punishment of two types, especially peer-punishment is considered to decrease the average payoff of all players as well as pool-punishment does, and to facilitate the antisocial punishment as a result of natural selection. To solve those problems, the author has proposed the probabilistic peer-punishment based on the difference of payoff. In the limited condition, the proposed peer-punishment has shown the positive effects on the evolution of cooperation, and increased the average payoff of all players. Based on those findings, this study exhibits the characteristics of the evolution of cooperation by the proposed peer-punishment. Those characteristics present the significant contribution to knowledge that for the evolution of cooperation, a limited number of players should cause severe damage to defectors at the large expense of their payoff when connections between them are sparse, whereas a greater number of players should share the responsibility to punish defectors at the relatively small expense of their payoff when connections between them are dense.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Valentina V. Tarasova, Vasily E. Tarasov A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their values at that time, but also on their values at previous times. For the mathematical description of the memory effects, we use the theory of derivatives of non-integer order. Crises are considered as sharp splashes (bursts) of the price, which are mathematically described by the delta-functions. Using the equivalence of fractional differential equations and the Volterra integral equations, we obtain discrete maps with memory that are exact discrete analogs of fractional differential equations of economic processes. We derive logistic map with memory, its generalizations, and “economic” discrete maps with memory from the fractional differential equations, which describe the economic natural growth with competition, power-law memory and crises.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): B. Samardzic, B.M. Zlatkovic The system consisting of several cascade connected electrical circuits is presented in this paper. Considering the system structure and the fact that the tunnel diodes have nonlinear characteristics, one of the properties of this system is the possibility of the chaos appearance. Necessary conditions and sufficient condition for the chaos appearance in the nonlinear cascade connected systems are given and analyzed, too. The results are confirmed by bifurcation and escape-time diagrams simulation.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Erivelton Geraldo Nepomuceno, Eduardo M.A.M. Mendes This paper reports the existence of more than one pseudo-orbit when simulating continuous nonlinear systems using a digital computer in a set-up different from the ones normally seen in the literature, that is, in a set-up where the step-size is not varied, the discretization scheme is kept the same as well as the initial conditions. Taking advantage of the roundoff error, a simple but effective method to determine a lower bound error and the critical time for the pseudo-orbits is used and the connection to the maximum (positive) Lyapunov exponent is established considering the bit resolution and the computational platform used for the simulations. To illustrate the effectiveness of the method and problems of using discretization schemes for simulating continuous nonlinear systems in a digital computer, the well-known Lorenz equations, the Rossler hyperchaos system, Mackey–Glass equation and the Sprott A system are used. The method can help the user of such schemes to keep track of the reliability of numerical simulations.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): J. Palanivel, K. Suresh, S. Sabarathinam, K. Thamilmaran We report the dynamics of a low dimensional fractional order forced LCR circuit using Chua’s diode. The stability analysis is performed for each segment of the piecewise linear curve of Chua’s diode and the conditions for the oscillation and double scroll chaos are obtained. The effect of fractional order on the bifurcation points are studied with the help of bifurcation diagrams. We consider both the derivatives of the systems current and voltage as fractional derivatives. When the order of the derivatives is decreased, the system exhibits interesting dynamical behavior. For instance, the value of the fractional order corresponding to the voltage is decreased, the chaotic regime in the system decreases. But in the case of current, the chaotic regime in the system increases initially and beyond a certain value of order, the chaotic regime decreases and extinguishes from the system. We found the lowest order for exhibiting chaos in the fractional order of the circuit as 2.1. For the first time, the experimental analogue of our proposed system is made by using the frequency domain approximation. The results are obtained from the experimental observations are compared with numerical simulations and found that they match closely with each other. The existence of chaos in the circuit is analyzed with the help of 0-1 test and power spectrum.

Abstract: Publication date: February 2017 Source:Chaos, Solitons & Fractals, Volume 95 Author(s): Fang Fang, Tayfun Babadagli The objective of this paper was to use laser imaging technique to visualize the diffusion controlled mass transfer process in porous media. Cubical models made of different materials (oil-wet plexiglass and water wet glass) and filled with 1mm and 4mm glass beads and different types of oils were used to visualize the -Fickian- diffusion of solvent with different densities and viscosities. 3-D visualization technique with laser sheet scanning of refractive index matched glass-bead-pack model was used to study the effect of permeability, solvent density, viscosity and boundary effect on mixing by diffusion. Three types of solvents were used: (1) solvent with density higher than oil but low viscosity, (2) solvent lighter than oil but has high viscosity, and (3) solvent lighter but less viscous than oil. It was observed through 3-D images obtained from the experiments that the width (area) of the solvent swept region and fingering depended on the density of the solvent and the speed of the process was higher in the high permeability porous media (4mm glass beads). Wider fingers and swept areas were observed for less viscous solvent. Solvents 1 and 2 slowly mixed and rose to the top of the model filling most of the pores in the model, and then diffused into the unswept region. Solvent 3 reached the top of the model in an extremely short time along the boundary with thin fingering and displaces downward afterwards. The frontal progresses of solvent-oil interfaces (mixing zone) were analyzed quantitatively through the change of the fractal dimension during the process. The fractal dimension increased before the solvent reached at the top of the model. For solvents 1 and 2, the fractal dimension decreased afterward. For solvent 3, the value declined rapidly because the solvent took time to spread along the top of the model due to its extremely low viscosity and density.