Youming Lei

Heteroclinic chaos in a Josephson-junction system perturbed by dichotomous noise excitation

The chaotic behavior in a Josephson-junction system perturbed by dichotomous noise excitation is discussed in detail. Conditions for the onsets of chaos are derived by virtue of the random Melnikov method together with the mean-square criterion. It is shown that with the increase of the noise transition rate, the threshold of the dichotomous noise amplitude for the onset of chaos in the system increases. The effects of dichotomous noise on the Josephson-junction system are also determined by numerical simulations via the mean largest Lyapunov exponents, which verifies that the injection of the dichotomous noise can cause the change of the sign of the largest Lyapunov exponent and lead to noise-induced chaos. Phase portraits and time histories are further used to verify these results. It can be concluded that by changing the internal parameters of the dichotomous noise, we can adjust the threshold for the onset of the chaos and then control dynamical behaviors in the Josephson-junction system subjected to dichotomous noise excitation.

Adaptive synchronization of an uncertain Qi system via only one scalar controller

The present paper addresses the problem of synchronization for the uncertain novel chaotic system (Qi system). Based on the Lyapunov stability theory and Barbalats lemma, an adaptive controller is proposed via only one scalar feedback to make the states of two identical Qi systems with unknown parameters asymptotically synchronized. Furthermore, all the unknown parameters can be estimated dynamically from the time series of the drive and response systems. Numerical simulations demonstrate the validity and feasibility of the proposed method.

Adaptive feedback synchronization of fractional-order complex dynamic networks

The aim of this paper is to investigate synchronization of fractional-order complex dynamic networks. To ensure synchronization of two dynamic networks, an adaptive feedback control method is proposed. With the stability analysis of the fractional-order differential system, we rigorously prove that the controller can make trajectory errors between the drive and response networks synchronized. The simple but practical method can be applied to a class of fractional-order networks without any prior analytical knowledge of the systems. Three illustrative examples are given to show the effectiveness of the proposed method.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Taming Chaotic Arrays By Parametric Excitation With Proper Random Phase

A weak harmonic parametric excitation with random phase has been introduced to tame chaotic arrays. It has been shown that when the amplitude of random phase properly increases, two different kinds of chaotic arrays, unsynchronized and synchronized, can be controlled by the criterion of top Lyapunov exponent. The Lyapunov exponent was computed based on Khasminskiis formulation and the extension of Wedigs algorithm for linear stochastic systems. In particular, it was found that with stronger coupling the synchronized chaotic arrays are more controllable than the unsynchronized ones. The bifurcation analysis, the spatiotemporal evolution, and the Poincare map were carried out to confirm the results of the top Lyapunov exponent on the dynamical behavior of control stability. Excellent agreement was found between these results.

Stochastic resonance in a non-smooth system under colored noise excitations with a controllable parameter

Stochastic resonance is studied in a class of non-smooth systems with a controllable parameter causing a change among monostability, bistability, and multistability, driven by colored noise. The system becomes smooth at a bifurcation point. Time scales in the non-smooth well are analyzed and transition rates of the non-smooth potential barriers are obtained. Analytical expressions for the response amplitude depending on the controllable parameter, frequency, noise intensity, and correlation time are derived in the bistable and multistable regions in the adiabatic limit. With the decrease of frequency, the optimal correlation time according to the maximum response is increasing; on the contrary, the optimal noise intensity is on the decline. Multistability of the system enhances the optimal transition rates and optimal response amplitude.

Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation

Fractional-order calculus is more competent than integer-order one when modeling systems with properties of nonlocality and memory effect. And many real world problems related to uncertainties can be modeled with stochastic fractional-order systems with random parameters. Therefore, it is necessary to analyze the dynamical behaviors in those systems concerning both memory and uncertainties. The period-doubling bifurcation of stochastic fractional-order Duffing (SFOD for short) system with a bounded random parameter subject to harmonic excitation is studied in this paper. Firstly, Chebyshev polynomial approximation in conjunction with the predictor-corrector approach is used to numerically solve the SFOD system that can be reduced to the equivalent deterministic system. Then, the global and local analysis of period-doubling bifurcation are presented, respectively. It is shown that both the fractional-order and the intensity of the random parameter can be taken as bifurcation parameters, which are peculiar to the stochastic fractional-order system, comparing with the stochastic integer-order system or the deterministic fractional-order system. Moreover, the Chebyshev polynomial approximation is proved to be an effective approach for studying the period-doubling bifurcation of the SFOD system.

DISORDER INDUCED ORDER IN AN ARRAY OF CHAOTIC DUFFING OSCILLATORS

This paper addresses the issue of disorder induced order in an array of coupled chaotic Duffing oscillators which are excited by harmonic parametric excitations. In order to investigate the effect of phase disorder on dynamics of the array, we take into account that individual uncoupled Duffing oscillator with a parametric excitation is chaotic no matter what the initial phase of the excitation is. It is shown that phase disorder by randomly choosing the initial phases of excitations can suppress spatio-temporal chaos in the system coupled by chaotic Duffing oscillators. When all the phases are the same and deterministic, the oscillators remain chaotic and asynchronous no matter what the common phase is. When driven asynchronously by introducing phase disorder, the oscillators coupled in the array appear more regular with increase of the amplitude of random phase, and the highest level of synchrony between them is induced by intermediate phase disorder, displaying a resonance like phenomenon caused from the transition of the coupled oscillators from chaos to periodic motion. Since varying the initial phases of excitations is more feasible than altering parameters intrinsic to the oscillators coupled in an array, this study provides a practical method for control and synchronization of chaotic dynamics in high-dimensional, spatially extended systems, which might have potential applications in engineering, neuroscience and biology.