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Jiguang Rao, Kuppuswamy Porsezian, Jingsong He
General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers, and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions...
August 2017: Chaos
Cesar Manchein, Rafael M da Silva, Marcus W Beims
In this work, we show how the composition of maps allows us to multiply, enlarge, and move stable domains in phase and parameter spaces of discrete nonlinear systems. Using Hénon maps with distinct parameters, we generate many identical copies of isoperiodic stable structures (ISSs) in the parameter space and attractors in phase space. The equivalence of the identical ISSs is checked by the largest Lyapunov exponent analysis, and the multiplied basins of attraction become riddled. Our proliferation procedure should be applicable to any two-dimensional nonlinear system...
August 2017: Chaos
T Congy, S K Ivanov, A M Kamchatnov, N Pavloff
We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations...
August 2017: Chaos
Jinjie Zhu, Xianbin Liu
In this paper, the collective behaviors for ring structured bursting neuronal networks with electrical couplings and distance-dependent delays are studied. Each neuron is modeled by the Hindmarsh-Rose neuron. Through changing time delays between connected neurons, different spatiotemporal patterns are obtained. These patterns can be explained by calculating the ratios between the bursting period and the delay which exhibit clear locking relations. The holding and the failure of the lockings are investigated via bifurcation analysis...
August 2017: Chaos
Hanshuang Chen, Chuansheng Shen, Haifeng Zhang, Jürgen Kurths
We theoretically study noise-induced phase switch phenomena in an inertial majority-vote (IMV) model introduced in a recent paper [Chen et al., Phys. Rev. E 95, 042304 (2017)]. The IMV model generates a strong hysteresis behavior as the noise intensity f goes forward and backward, a main characteristic of a first-order phase transition, in contrast to a second-order phase transition in the original MV model. Using the Wentzel-Kramers-Brillouin approximation for the master equation, we reduce the problem to finding the zero-energy trajectories in an effective Hamiltonian system, and the mean switching time depends exponentially on the associated action and the number of particles N...
August 2017: Chaos
P R Venkatesh, A Venkatesan, M Lakshmanan
We have used a system of globally coupled double-well Duffing oscillators under an enhanced resonance condition to design and implement Dual Input Multiple Output (DIMO) logic gates. In order to enhance the resonance, the first oscillator in the globally coupled system alone is excited by two forces out of which one acts as a driving force and the other will be either sub-harmonic or super-harmonic in nature. We report that for an appropriate coupling strength, the second force coherently drives and enhances not only the amplitude of the weak first force to all the coupled systems but also drives and propagates the digital signals if any given to the first system...
August 2017: Chaos
Debsankha Manik, Marc Timme, Dirk Witthaut
We study multistability in phase locked states in networks of phase oscillators under both Kuramoto dynamics and swing equation dynamics-a popular model for studying coarse-scale dynamics of an electrical AC power grid. We first establish the existence of geometrically frustrated states in such systems-where although a steady state flow pattern exists, no fixed point exists in the dynamical variables of phases due to geometrical constraints. We then describe the stable fixed points of the system with phase differences along each edge not exceeding π/2 in terms of cycle flows-constant flows along each simple cycle-as opposed to phase angles or flows...
August 2017: Chaos
Fei Xiong, Yun Liu, Liang Wang, Ximeng Wang
To reveal heterogeneous behaviors of opinion evolution in different scenarios, we propose an opinion model with topic interactions. Individual opinions and topic features are represented by a multidimensional vector. We measure an agent's action towards a specific topic by the product of opinion and topic feature. When pairs of agents interact for a topic, their actions are introduced to opinion updates with bounded confidence. Simulation results show that a transition from a disordered state to a consensus state occurs at a critical point of the tolerance threshold, which depends on the opinion dimension...
August 2017: Chaos
Ignacio S Gomez, M Portesi, P W Lamberti
We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d¯ for an arbitrary discrete map. Moreover, from d¯, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity...
August 2017: Chaos
Ivan A Korneev, Vladimir V Semenov
The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined with the bifurcational analysis. It has been shown that the oscillation excitation has distinctive features of the supercritical Andronov-Hopf bifurcation and can be achieved by changing of a parameter value as well as by variation of initial conditions. Therefore, the considered bifurcation is called Andronov-Hopf bifurcation with and without parameter...
August 2017: Chaos
José M Amigó, Yoshito Hirata, Kazuyuki Aihara
In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy...
August 2017: Chaos
Zhongkui Sun, Jintian Zhang, Xiaoli Yang, Wei Xu
The dynamics in fractional-order systems have been widely studied during the past decade due to the potential applications in new materials and anomalous diffusions, but the investigations have been so far restricted to a fractional-order system without time delay(s). In this paper, we report the first study of random responses of fractional-order system coupled with noise and delayed feedback. Stochastic averaging method has been utilized to determine the stationary probability density functions (PDFs) by means of the principle of minimum mean-square error, based on which stochastic bifurcations could be identified through recognizing the shape of the PDFs...
August 2017: Chaos
Jung-Wan Ryu, Jong-Ho Kim, Woo-Sik Son, Dong-Uk Hwang
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case...
August 2017: Chaos
Yong Sun, Jürgen Kurths, Meng Zhan
Power grids and their properties have been studied broadly in many aspects. In this paper, we propose a novel concept, power-flow-based power grid, as a typical power-functional network, based on the calculation of power flow distribution from power electrical engineering. We compare it with structural networks based on the shortest path length and effective networks based on the effective electrical distance and study the relationship among these three kinds of networks. We find that they have roughly positive correlations with each other, indicating that in general any close nodes in the topological structure are actually connected in function...
August 2017: Chaos
Maria Teodora Ferreira, Rosangela Follmann, Margarete O Domingues, Elbert E N Macau, István Z Kiss
Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation...
August 2017: Chaos
D V Verveyko, A Yu Verisokin, E B Postnikov
We study the influence of periodic influx on a character of glycolytic oscillations within the forced Selkov system. We demonstrate that such a simple system demonstrates a rich variety of dynamical regimes (domains of entrainment of different order (Arnold tongues), quasiperiodic oscillations, and chaos), which can be qualitatively collated with the known experimental data. We determine detailed dynamical regimes exploring the map of Lyapunov characteristic exponents obtained in numerical simulations of the Selkov system with periodic influx...
August 2017: Chaos
Junhao Peng, Elena Agliari
Fractal (or transfractal) features are common in real-life networks and are known to influence the dynamic processes taking place in the network itself. Here, we consider a class of scale-free deterministic networks, called (u, v)-flowers, whose topological properties can be controlled by tuning the parameters u and v; in particular, for u > 1, they are fractals endowed with a fractal dimension df, while for u = 1, they are transfractal endowed with a transfractal dimension d̃f. In this work, we investigate dynamic processes (i...
August 2017: Chaos
David Coufal, Jozef Jakubík, Nikola Jajcay, Jaroslav Hlinka, Anna Krakovská, Milan Paluš
Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed-the method based on conditional mutual information-the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping-the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method...
August 2017: Chaos
Chunbiao Li, Julien Clinton Sprott, Akif Akgul, Herbert H C Iu, Yibo Zhao
A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system...
August 2017: Chaos
XiaoLi Yang, YanHu Yu, ZhongKui Sun
This study investigates the nontrivial effects of autapse on stochastic resonance in a modular neuronal network subjected to bounded noise. The resonance effect of autapse is detected by imposing a self-feedback loop with autaptic strength and autaptic time delay to each constituent neuron. Numerical simulations have demonstrated that bounded noise with the proper level of amplitude can induce stochastic resonance; moreover, the noise induced resonance dynamics can be significantly shaped by the autapse. In detail, for a specific range of autaptic strength, multiple stochastic resonances can be induced when the autaptic time delays are appropriately adjusted...
August 2017: Chaos
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