Abstract: Publication date: August 2018Source: Chaos, Solitons & Fractals, Volume 113Author(s): Jingshou Liu, Wenlong Ding, Junsheng Dai, Gang Zhao, Yaxiong Sun, Haimeng YangAbstractFractal theory has been widely applied in a variety of disciplines to understand the theory behind chaotic phenomena based on internal self-similarity. In this study, three ideal geological models are used to analyze the unreliability of the capacity dimension in the fractal calculation of geological bodies with different scales. Additionally, by varying the side length r of the statistical units, the geological meanings of the fractal dimension D and the correlation coefficient R2 are discussed. The points of information (POIs) are densely filled by binarizing the geological bodies to black/white. Based on the optimized r of a geological body, an algorithm is derived that divides the grids of the statistical units to determine the probability of the POIs falling into different grids. The information dimension (DI) and R2 of a geological body are obtained by fitting the variable data. An example calculation of the information dimension field in the Jinhu sag is presented to demonstrate the methodology and to test its reliability. The results show that determining the appropriate side length of the statistical unit is key to evaluating the fractal calculation. Compared to the capacity dimension, DI is more reliable in the fractal calculation of multi-scale geological bodies; DI is thereby the preferred fractal dimension to use in the analyses of these types of geological bodies.

Abstract: Publication date: August 2018Source: Chaos, Solitons & Fractals, Volume 113Author(s): Antonio Algaba, Cristóbal García, Manuel ReyesAbstractWe solve, by using normal forms, the analytical integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system whose origin is an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x˙=x(P2+P3),y˙=y(Q2+Q3), with Pi, Qi homogeneous polynomials of degree i. We also prove that for any n ≥ 3, there are analytically integrable perturbations of x˙=xPn,y˙=yQn which are not orbital equivalent to its first homogeneous component.

Abstract: Publication date: August 2018Source: Chaos, Solitons & Fractals, Volume 113Author(s): Jia He, Yumei XueAbstractIn this paper, we construct the evolving networks from hollow cube in fractal geometry by encoding. We set the unit cubes as nodes of network, where two nodes are neighbors if and only if their corresponding cubes have common surface. We also study some characteristics of the network, such as degree distribution, clustering coefficient and average path length. We obtain this network with small world and scale-free properties by the self-similar structure.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Sajad Jafari, Soroush Dehghan, Guanrong Chen, Sifeu Takougang Kingni, Karthikeyan RajagopalAbstractThis paper introduces a chaotic system in the spherical coordinates which, when expressed in the Cartesian coordinate system, has a chaotic attractor located in an impassable sphere like a bird in the cage. It also has a coexisting attractor outside that sphere. Basic dynamical properties of this system are investigated and its FPGA realization is demonstrated.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): F. Panichi, G. TurchettiAbstractWe discuss the stability of a Hamiltonian system by comparing the standard Lyapunov error (LE) with the forward error (FE) due to a small random perturbation. We introduce also the reversibility error (RE) where the evolution is computed forward up to time t and backwards to t=0 in presence of noise. This procedure has been investigated in the case of symplectic maps, but it turns out that the results are simpler in the case of a noisy flow, in the limit of zero noise amplitude. Indeed the stochastic processes defined by the displacement of the noisy orbit at time t for FE, or at time 0 for RE after the evolution up to time t, satisfy linear Langevin equations, are Gaussian processes, and the errors are just their root mean square deviations. All the errors are expressed in terms of the fundamental matrix L(t) of the tangent flow and can be evaluated numerically using a symplectic integrator. Letting eL(t) be the Lyapunov error and eR(t) be the reversibility error a very simple relation holds eR2(t)=∫0teL2(s)ds. The integral relation is quite natural since the local errors due to a random perturbations accumulate during the evolution whereas for the Lyapunov case the error is introduced only at time zero and propagated. The plot of errors for initial conditions in a Poincaré section reflects the phase portrait, whereas in the action plane it allows to single out the resonance strips. We have applied the method to a 3D Hamiltonian model H=H0(J)+λV(Θ), where analytic estimates can be obtained for the single resonances from perturbation theory. This allows to inspect the double resonance structure where the single resonance strips intersect. We have also considered the Hénon–Heiles Hamiltonian to show numerically the equivalence of the errors apart from a shift of 1/2 in the power law exponent in the case of regular orbits. The reversibility error method (REM), previously introduced as the error due to round off in the symplectic integration, appears to be comparable with RE also for the models considered here.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Zhenxi Niu, Jiwei Xu, Dameng Dai, Tairan Liang, Deming Mao, Dawei ZhaoAbstractIn this paper, we explore the effects of rational conformity behavior on the evolution of cooperation in prisoner's dilemma. In general, we think individual updates strategy is based on the difference in income between himself and his neighbors. In real life, in order to avoid risks, they may be consistent with most individuals in the group, because they are not the worst. Therefore, we divide the players into two categories, one is traditional players and the other is rational conformists who update their strategies are based on the two factors: payoffs and the behavior of most individuals in their nearest neighbors. Through a large number of simulations, we find that, rational conformity behavior can promote cooperation in the prisoner's dilemma game, and the greater the proportion of rational players, the more obvious the promotion of cooperation. Our work may provide further insight in understanding the evolution of cooperation, players selectively follow others and make some adjustments according to the current environment to make their own situation better.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Sizhong Zhou, Hongxia Liu, Tao ZhangAbstractMany problems on computer science, chemistry, physics and network theory are related to factors, factorizations and orthogonal factorizations in graphs. For example, the telephone network design problems can be converted into maximum matchings of graphs; perfect matchings or 1-factors in graphs correspond to Kekulé structures in chemistry; the file transfer problems in computer networks can be modelled as (0, f)-factorizations in graphs; the designs of Latin squares and Room squares are related to orthogonal factorizations in graphs; the orthogonal (g, f)-colorings of graphs are related to orthogonal (g, f)-factorizations of graphs. In this paper, the orthogonal factorizations in graphs are discussed and we show that every bipartite (0,mf−(m−1)r)-graph G has a (0, f)-factorization randomly r-orthogonal to n vertex disjoint mr-subgraphs of G in certain conditions.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Mohammad Hossein Heydari, Zakieh AvazzadehAbstractIn this study, the Poisson equation is generalized with the concept of variable-order (V-O) fractional derivatives called variable-order fractional Poisson equation (V-OFPE). In order to find an accurate solution of this system, we establish an optimization method through the Legendre wavelets (LWs). To carry out the method, we firstly derive an operational matrix (OM) of V-O fractional derivative for the LWs to be employed in expanding the unknown solution. Then, the function of residual is applied to reform the V-OFPE to an optimization problem which leads to choose the unknown coefficients optimally. In the final step, we implement the constrained extremum method which adjoins the objective function implied from the two-norm of residual function and the constraints corresponded to the given boundary conditions by a set of Lagrange multipliers. Accordingly, the final optimal conditions are actually the algebraic equations including the expansion coefficients and Lagrange multipliers. Theoretical convergence and error analysis of the approximation procedure using the LWs are investigated. In addition, the applicability and computational efficiency are experimentally examined for some illustrative examples.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Haide Gou, Baolin LiAbstractThis paper is concerned with the fractional differential equations of Sobolev type with boundary conditions in a Banach space. With the help of properties of Hilfer fractional calculus, the theory of propagation family as well as the theory of the measure of noncompactness and the fixed point methods, we obtain the existence results of mild solutions for Sobolev type fractional evolution differential equations involving Hilfer fractional derivative. Finally, two examples are presented to illustrate the main result.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Cong Wang, Hongli Zhang, Wenhui Fan, Ping MaAbstractChaotic oscillation in a power system is considered the main cause of power blackouts in large-scale interconnected power grids. The chaotic oscillation mechanisms and the control methods for chaos oscillation of power systems need to be analyzed. This paper thus proposed an adaptive control method for chaotic power systems using finite-time stability theory and passivity-based control approach. The adaptive feedback controller is first constructed using the finite-time stability theory and the passive theory to make the chaotic power system equivalent to a closed-loop passive system. We then proved that the passive power system can stabilize the equilibrium points. We also extensively studied fourth-order power system. Results show that the controller based on the finite-time theory and the passivity-based control approach can effectively stabilize the chaotic behavior within finite time. The control strategy was also found to be robust to the different power system states.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Tong Luo, Ming Xu, Yunfeng DongAbstractA two-dimensional hyperbolic Hamiltonian system can be linearly stabilized by a Hamiltonian structure-preserving controller. A linear symplectic transformation and the Lie series method can successfully normalize the expanded Hamiltonian function around a controlled stable equilibrium point, then the dynamics in the controlled center manifolds of which can be described by a Poincaré section. With the implement of the inverse transformation of the Lie series, the analytical results of the controlled manifolds can be obtained. Applying normalization and analytical calculation to planar solar sail three-body problem, we can get the normal form of the corresponding Hamiltonian function and trajectory around the chosen equilibrium point by analytical results. Finally, typical KAM theory is used to analyze the nonlinear stability of the controlled equilibrium point, and the stable region of the control gains are given by numerical calculation.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Juanhui Zheng, Baotong CuiAbstractIn this paper, we address the problem of state estimation of the Lurie system via the communication channel in the case of only this system outputs available. A coder-decoder scheme combines with a logarithmic quantization to form a novel and reliable communication channel. The errors between Lurie system outputs and observer outputs are regarded as the feedback signals, which are transmitted into the observer though the communication channel. A sufficient condition for input-to-state stability is given for the boundedness of the error of state estimation. The results of two examples show the effectiveness and superiority of the proposed communication channel of the logarithmic quantization.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Dongmei Huang, Wei Li, Guidong Yang, Meijuan HeAbstractIn this paper, the dynamical properties of a real-power vibration isolation system with delayed feedback control subjected to deterministic and stochastic excitations are considered. According to the free vibration analysis, it is found that a large number of limit cycles may be existed for certain time delay and feedback gain. Then, the relationship of amplitude and frequency is derived for the undamped system. For the system with harmonic excitation, multi-valued phenomena are observed due to the existence of the limit cycles. In this respect, with the change of time delay, in every period the response is similar to time delay island, and the number of islands is different under different excitation frequency. Additionally, for analyzing the complex dynamic properties, the vibration isolation system with Gauss white noise excitation is explored by the largest Lyapunov exponent and the stationary probability density. The symmetrical period-doubling bifurcation phenomenon is found and verified. Finally, by using Monte Carlo simulation, the stationary probability density is explored from original system. The change of time delays can induce the occurrence of stochastic bifurcation and the response from two peaks becomes triple peaks.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Navid Vafamand, Shapour Khorshidi, Alireza KhayatianAbstractThis paper proposes a novel hyperchaotic secure communication scheme for non-ideal communication channels. The proposed approach employs Takagi–Sugeno (TS) fuzzy model and linear matrix inequality (LMI) technique to design a controller which synchronizes the hyperchaotic transmitter and receiver systems. In the presented method, only few numbers of states are needed to be transformed which is consistent with the practical limitations of a non-ideal channel and highly secure communication. Therefore, a robust fuzzy observer is proposed to estimate the other states of the transmitter at the receiver side. Furthermore, since the channel is non-ideal, H∞ performance criterion is employed to derive robust observer and controller against the external disturbance and noise. In order to make the proposed approach more applicable, the sufficient controller and observer design conditions are formulated in terms of linear matrix inequalities (LMIs) which can be solved by convex optimization techniques. In addition, to further remove the effect of the noise on the information recovery, a moving average filter is utilized. Finally, to show the effectiveness and advantages of the proposed approach, the hyperchaotic Lorenz system is considered and the signal is analyzed at the transmitter and receiver sides. Then, the results obtained show the superiority and effectiveness of the proposed method compared with those of the existing approaches.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Xingyu HanAbstractWe explore the valuation and hedging strategies of a European vulnerable option with funding costs and collateralization for local volatility models. It is found that, in the absence of arbitrage opportunities, the option price must lie within a no-arbitrage band. The boundaries of no-arbitrage band are computed as solutions to backward stochastic differential equations (BSDEs in short) of replicating strategy and offsetting strategy. Under some conditions, we obtain the closed-form representations of the no-arbitrage band for local volatility models. In particular, the fully explicit expressions of the no-arbitrage band for Black–Scholes model and the constant elasticity of variance (CEV) model with time-dependent parameters are derived. Furthermore, we provide a strategy for the option holder by using the risky bond issued by the option writer to hedge the remaining potential losses. By virtue of numerical simulation, the impact of the default risk, funding costs and collateral can be observed visually.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Mingyuan Zhang, Boyuan Liang, Sheng Wang, Matjaž Perc, Wenbo Du, Xianbin CaoAbstractThe increase in economic exchange, brought about by globalization and leaps of progress in science and engineering, has led to a sharp increase in air traffic density. As a consequence, airspace has become increasingly crowded, and limitations in airspace capacity have become a major concern for the future development of air travel and transportation. In this paper, we adopt methods of network science to analyze flight conflicts in the Chinese air route network. We show that air conflicts are distributed heterogeneously along the waypoints of the Chinese air route network. In particular, the frequency of flight conflicts follows an exponential distribution. The time-space investigation of flight conflicts shows that they are concentrated at specific regions of the Chinese air route network and at specific time periods of the day. Our work offers fascinating insights into one of the world's largest and most busiest air route networks, and it helps us mitigate flight conflicts and improve air traffic safety.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Pengfei Xu, Yanfei JinAbstractThis paper investigates the mean first-passage times (MFPTs) of a delayed tristable system driven by correlated multiplicative and additive noises. The results suggest that the correlation between the multiplicative and additive noises can induce symmetry-breaking in the delayed tristable system. The noise-induced dynamics, such as the noise enhanced stability (NES) and the resonant activation (RA), can be observed with considering the combined influences of correlated noises and intermediate stable state. The time delay plays an important role in the MFPTs. For example, with respect to the middle well, the increase of time delay results in the weakening of the stability of the two lateral wells; thus, all the MFPTs are decreased notably. Moreover, a law of MFPTs is established for three different potential wells. That is, the MFPT T(s1 → s3) (between the left and right wells) is equal to the sum of T(s1 → s2) (from left well to middle one) and T(s2 → s3) (from middle well to right one). However, this change regulation can be first broken with an increase in time delay, and then restored with the increase of correlation between noises.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Sajad Ali, Mushtaq Ahmad, M. FarooqAbstractIn the present article coupled drift-ion acoustic mode is investigated in four component collisional, magnetized, and inhomogeneous ambiplasma consisting of positive and negative ions, non-thermal electrons and positrons. Linear dispersion relation for the coupled mode is derived with effect of nothermality and particle concentration. In the presence of weak dispersion and dissipation a KdV-Burger equation is derived in nonlinear regime, for coupled acoustic-drift shock and soliton. Using Tanh-method the solution for double layers in the system is derived. The results are numerically highlighted for ambi plasma at early universe and space plasma. Further more keeping in view the non thermal behavior of ambiplasma in space, a kappa distributed approach is used for these calculations.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): S. Ijaz, S. NadeemAbstractThe present research article is focused to analyze the blood mediated nanoparticle transportation through the atherosclerotic artery. The wall property on the atherosclerotic artery is also assumed to create resemblance with permeability characteristic of the arterial wall thickness. Heat transfer property of the catheter wall as well as the arterial wall is taken into account for the purpose to attenuate the stenotic lesions. To discuss the problem, mathematical model is developed through phase flow approach with hybrid nanofluid phenomena. Arterial pressure in the stenotic artery is also discussed through tapering impacts. Further, flow configurations of hemodynamics are evaluated to discuss the flow of blood through atherosclerotic artery. The outcomes obtained in this analysis are useful in biomedical related application. It is concluded from this mathematical problem through graphical results that the use of Cu–Al2O3/blood is more suitable to reduce the resistance to flow of the atherosclerotic artery when compared to the case of Cu-blood. Moreover, a wall properties impact depicts that hemodynamics of atherosclerotic artery increases.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Payam Sadeghi Shabestari, Shirin Panahi, Boshra Hatef, Sajad Jafari, Julien C. SprottAbstractFor non-invasively investigating the interaction between insulin and glucose, mathematical modeling is very helpful. In this paper, we propose a new model for insulin-glucose regulatory system based on the well-known prey and predator models. The results of previous researches demonstrate that chaos is a common feature in complex biological systems. Our results are in accordance with previous studies and indicate that glucose-insulin regulatory system has various dynamics in different conditions. One interesting feature of this new model is having hidden attractor for some set of parameters. The result of this paper might be helpful for better understanding of regulatory system that contains glucose, insulin, and diseases such as diabetes, hypoglycemia, and hyperinsulinemia.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Márcia L.C. Peixoto, Erivelton G. Nepomuceno, Samir A.M. Martins, Márcio J. LacerdaAbstractIt has been shown that natural interval extensions (NIE) can be used to calculate the largest positive Lyapunov exponent (LLE). However, the elaboration of NIE are not always possible for some dynamical systems, such as those modelled by simple equations or by Simulink-type blocks. In this paper, we use rounding mode of floating-point numbers to compute the LLE. We have exhibited how to produce two pseudo-orbits by means of different rounding modes; these pseudo-orbits are used to calculate the Lower Bound Error (LBE). The LLE is the slope of the line gotten from the logarithm of the LBE, which is estimated by means of a recursive least square algorithm (RLS). The main contribution of this paper is to develop a procedure to compute the LLE based on the LBE without using the NIE. Additionally, with the aid of RLS the number of required points has been decreased. Eight numerical examples are given to show the effectiveness of the proposed technique.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Zhiying Chen, Yong Liu, Ping ZhouAbstractFractal dimension is the most important parameter for surface characterization. In this paper, four methods used to estimate the fractal dimensions of surface profiles and their applications in machined surfaces are studied. These methods are first evaluated using surface profiles created by Weierstrass–Mandelbrot function from the three aspects of fitting accuracy, calculation accuracy and calculation stability, and then applied to the machined rough surfaces. By comparing the results of the four methods, it is found that none of the methods is particularly prominent in all of the three aspects. However, the three point sinuosity method is found to be relatively the most suitable and reliable method among the four tested methods for extracting fractal dimensions of both generated and measured rough surface profiles.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): B. Nana, S.B. Yamgoué, R. Tchitnga, P. WoafoAbstractWe report the modeling for analysis of electrical clippers with side to side oscillating blade. The mathematical expressions for the study of its electromechanical dynamics are derived from the application of electromagnetics as well as mechanics laws. Numerical and analytical investigations reveal that, for well chosen range of its control parameters the efficiency of such clippers can be significantly improved, while the electrical power consumption is optimized. Chaotic behavior is investigated numerically using bifurcations diagrams. Experimental results match up well the theoretical predictions.

Abstract: Publication date: July 2018Source: Chaos, Solitons & Fractals, Volume 112Author(s): Xiaohui Dong, Ming Wang, Guang-Yan Zhong, Fengzao Yang, Weilong Duan, Jiang-Cheng Li, Kezhao Xiong, Chunhua ZengAbstractIn this paper, the stochastic kinetics in a time-delayed foraging colony system under non-Gaussian noise were investigated. Using delay Fokker–Planck approach, the stationary probability distribution (SPD), the normalized variance β2, skewness β3 and kurtosis β4 of the state variable are obtained, respectively. The effects of the time delayed feedback and non-Gaussian noise on the SPD are analyzed theoretically. The numerical simulations about the SPD are obtained and in good agreement with the approximate theoretical results. Furthermore, the impacts of the time delayed feedback and non-Gaussian noise on the β2, β3 and β4 are discussed, respectively. It is found that the curves in β2, β3 and β4 exhibit an optimum strength of feedback where β2, β3 and β4 have a maximum. This maximum indicates the large deviations in β2, β3 and β4. From the above findings, it is easy for us to have a further understanding of the roles of the time delayed feedback and non-Gaussian noise in the foraging colonies system.