One of the most interesting problems is investigation boundaries chaotic or hyperchaotic systems. In addition to estimating Lyapunov and Hausdorff dimensions, it can be applied in chaos control synchronization. this paper, by means analytical optimization, comparison principle, generalized function theory, we find ultimate bound set for a new six-dimensional system globally exponentially attrac...

This paper presents hyperchaos anti-synchronization of different hyperchaotic systems using Active Generalized Backstepping Method (AGBM). The proposed technique is applied to achieve hyperchaos antisynchronization for the Lorenz and Lu dynamical systems. Generalized Backstepping Method (GBM) is similarity to Backstepping and more applications in systems than it. Bckstepping method is used only...

Synchronization of chaotic systems has aroused much interest in recent years, particularly in light of potential application of this phenomenon in secure communication. Different approaches for constructing synchronized chaotic systems are proposed. Among them is the approach of Pecora and Carroll [1990] who show that when a state variable from a chaotically evolving system is transmitted as an...

A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchro...

The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of noise, enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system. The method is dem...

Abstract. In chaotic cryptosystems, it is recognized that using (very) high dimensional chaotic attractors for encrypting a given message may improve the privacy of chaotic encoding. In this paper, we study a kind of hyperchaotic systems using some classical methods. The results show that besides the high dimension, the sub-Nyquist sampling interval is also an important factor that can improve ...

The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynam...