Generation and Modified Projective Synchronization for a Class of New Hyperchaotic Systems

Abstract

A class of new hyperchaotic systems with different nonlinear terms is proposed, and the existence of hyperchaos is exhibited by calculating their Lyapunov exponent spectrums. Then the universal theories on modified projective synchronization (MPS) of the systems with general form which linearly depends on unknown parameters or time-varying parameters, are investigated by presenting an adaptive control strategy together with parameter update laws and a nonlinear control scheme based on Lyapunov stability theory. Subsequently, the presented control methods are applied to achieve MPS of the new hyperchaotic systems, and their effectiveness is illustrated by numerical simulations.

A research on adaptive control to stabilize and synchronize a hyperchaotic system with uncertain parameters

“…At present, there are different kinds of control methods and techniques that have been proposed for carrying out chaos control and synchronization of chaotic dynamical systems. These include the active control techniques [6], adaptive control [7], modified projective synchronization [8], linear feedback control [9] and the sliding mode control [10], which are worth citing here among others. [11][12][13].…”

“…Recently, Jia et al [8] proposed and investigated a class of new hyperchaotic systems that contain two cross product terms and a quadratic term. The hyperchaotic systems [8] show rich complex dynamics.…”

“…Recently, Jia et al [8] proposed and investigated a class of new hyperchaotic systems that contain two cross product terms and a quadratic term. The hyperchaotic systems [8] show rich complex dynamics. The modified projective synchronization of the disturbance free hyperchaotic systems with general form which linearly depends on uncertain parameters, are investigated by presenting an adaptive control technique together with parameter update laws and a nonlinear control scheme based on the Lyapunov stability theory.…”

“…In this paper, the authors further investigated the stabilization of hyperchaos at one of its equilibrium point at the origin and complete synchronization behavior of uncertain hyperchaotic system [8] in the presence of external disturbance. To the best of the authors' knowledge, this problem has not been discussed before.…”

Generalized Outer Synchronization between Complex Networks with Unknown Parameters

“…However, if the purpose is only to show that there exists GS on networks rather than the exact functional relations, this approach is efficient for investigation of GS on complex networks. Some recent work [10,[17][18][19][20][21][22][23] has studied generalized outer synchronization (GOS) in complex networks or complex systems, where the node dynamics parameters are known in advance. Nevertheless, in many practical situations, it is common that some system parameters cannot be exactly known in prior, and the synchronization will be destroyed and broken by the effects of these uncertainties.…”