Synchronization in chaotic systems has particular interest in the past few years; it has many applications, especially in secure communications (Carroll & Pecora, 1991; Chua et al, 1992; Ogorzalek, 1993; Chen, 1997; Bai & Lonngren, 1997). Fujisaka and Yamada noticed that ‘by coupling together oscillators which on their own evolved chaotically, it was possible under certain circumstances to forc...

Hyperchaotic systems are chaotic systems having more than one positive Lyapunov exponent and they have important applications in secure data transmission and communication. This paper applies active control method for the synchronization of identical and different hyperchaotic Pang systems (2011) and hyperchaotic Wang-Chen systems (2008). Main results are proved with the stability theorems of L...

X iv :n lin /0 40 60 31 v2 [ nl in .C D ] 1 7 Ju n 20 04 Inherent Frequency and Spatial Decomposition of the Lorenz Chaotic Attractor Gonzalo Álvarez, † Shujun Li, ‡ Jinhu Lü, and Guanrong Chen Instituto de F́ısica Aplicada, Consejo Superior de Investigaciones Cient́ıficas, Serrano 144—28006 Madrid, Spain Department of Electronic Engineering, City University of Hong Kong, Kowloon Toon, Hong Kong,...

In this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (HOAMSC). It is proved that the proposed controller is robust to m...

The substitution box (S-box) is found in many block cipher, and it is a very important component. Since the chaotic system has several significant advantageous properties desirable for cryptosystem, the design of S-box using chaos has attracted a great deal of attention in recent years. In this paper, a novel method for designing key-dependent S-boxes based on a four-dimensional hyperchaotic Ch...

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the syste...

Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.