Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization (FPS) in drive-response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.     

Generalized projective synchronization of two coupled complex networks of different sizes

We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach.     

Studying the intermittent stable theorem and the synchronization of a delayed fractional nonlinear system

In this paper, an intermittent synchronizing delayed fractional nonlinear system is studied. We propose a novel intermittent stable theorem for the delayed fractional system and derive a new synchronization criterion for delayed fractional systems by means of fractional stable theorem and the differential inequality method. Intermittent synchronizing fractional delayed Newton-Leipnik system is taken as an illustrative example and numerical simulation of this example is presented to show the feasibility and effectiveness of the proposed theorem.     

Complete synchronization induced by disorder in coupled chaotic lattices

The effect of phase disorder in external forces introduced into two-dimensional lattices of coupled chaotic pendulums is investigated. As the increase of the disorder, we find complete synchronization between the pendulums in each chain and different periodic synchronized patterns, while the chain remains asynchronous if all driving forces have the same phase. Applying the master stability function method, an analytic solution is given to support the numerical results. All these findings may provide further insight into chaos control and synchronization in nonlinear systems.     

Noise-Induced Resonance in Bistable Systems Caused by Delay Feedback

Abstract

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one-dimensional parametrized stochastic differential equation with point delay; the basic properties of which we check.

With a view to capturing the effective dynamics and, in particular, the resonance-like behavior of the reference model, we construct a simplified or reduced model, the two-state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance.

Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two-state model and the reference model. The resonance characteristics developed for the reduced model can thus be applied to the original model.     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

Influence of injection patterns on chaos synchronization performance between a multimode laser diode and a single-mode laser

In this paper, based on a system composed of a multimode emitted laser diode and a single-mode received laser, chaos synchronization performance has been investigated numerically under different optical injection patterns. The results show that, for single mode injection (SMI) which means the received laser is injected by a selective longitudinal mode of the multimode emitted laser whose wavelength corresponds to that of the single-mode received laser, the system synchronization performance is better than that with multi mode injection (MMI); depending on the optical spectrum of the received laser, the physical mechanism of chaos synchronization deterioration for MMI is given. Additionally, after taking into account the parameter mismatches, the chaos synchronization performance of the system with different injection pattern have also been discussed. For either SMI or MMI, the synchronization performance with negative parameter mismatches is better than that with positive parameter mismatches.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

In this Letter, a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization” of a class of fractional-order chaotic systems via a scalar transmitted signal. This synchronization approach is theoretically and numerically studied. By using stability theory of linear fractional-order systems, the suitable conditions for achieving synchronization are given. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.