This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very usefu...

The seminal papers by Pecora and Carrol (PC) [1] and Ott, Grebogi and Yorke (OGY) [2] in 1990 have induced avalanche of research works in the field of chaos control. Chaos synchronization in dynamical systems is one of methods of controling chaos, see, e.g. [1-8] and references therein.The interest to chaos synchronization in part is due to the application of this phenomenen in secure communica...

In this paper, we propose a simple method for chaos synchronization in discrete-time, based on new criterion for stability. This criterion implying the Lyapunov stabilization criterion, and is applicable to some typical chaotic systems. Keywords: Chaos synchronization, dynamical systems, new criterion, discrete-time, Lyapunov stability 1 Introduction During the last decade, synchronization of c...

In this paper, the adaptive synchronization method of three coupled identical chaos systems is proposed. New generic criteria of global chaos synchronization and strict theoretical proofs are given. The unidirectional (bidirectional) coupled system will synchronize by adding three adaptive feedback gain equations. As an example, the three Rössler chaotic systems with unidirectional coupling are...

In this paper a variety of uncertainty phenomena in chaos synchronization, which are caused by the sensitive dependence on initial conditions and coupling strength, are numerically investigated. Two identical Chua’s circuits are considered for both mutuallyand unidirectionallycoupled systems. It is found that initial states of the system play an important role in chaos synchronization. Dependin...

This paper discusses a circuit family including a dependent switched capacitor (DSC). The DSC function is instantaneously short of one capacitor at the moment when its voltage reaches a threshold. The chaos generation can be guaranteed theoretically, We also consider a master-slave system. If there does not exist a homoclinic orbit in the master chaos attractor, it exhibits either in-phase or i...

Since the beginning of the 90s a new direction appeared in the theory of dynamical systems, which was called “Controlling chaos”. The subject of this field is how to transform chaotic behavior to a regular one or to a more simple chaotic one by means of special small influence on the dynamical system. Pioneer works of this new direction were papers by Hubler and Lucher [1989], Jackson [1990] an...

This paper investigates the adaptive chaos control and synchronization of the Shaw chaotic system (Shaw, 1981) with unknown parameters. First, we design adaptive control laws to stabilize the Shaw chaotic system with unknown parameters to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve gl...

We give the relationship between symbolic dynamics and chaos synchronization. If the capacity of the channel which onedirectionally connects two chaotic systems with the aim of synchronizing them is larger than Kolmogorov–Sinai entropy of the driving system, then the synchronization error can be made arbitrarily small.

Many chaotic oscillators have rather coherent phase dynamics but strong fluctuation in the amplitudes. Conversely, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals. We study the effects of noise on the synchronization of homoclinic chaos to a weak periodic signal and demonstrate numerically and experimentally in a CO2 laser system that noi...