Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure

Abstract

Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive control method. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

“…Since the seminal work of Pecora and Carroll [1], chaos synchronization has been an active topic in nonlinear science, due to its potential applications in secure communication, control theory, telecommunications, biological networks and artificial neural networks, and so forth. So far, many effective approaches have been presented to synchronize chaotic systems such as adaptive control [2,3], fuzzy control [4], static feedback control [5], variable structure control [6], stochastic control [7], impulsive control [8][9][10], and others. Impulsive control, as a discontinuous control method, has attracted more interest recently due to its easy implementation in engineering control.…”