Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control

TL;DR

This paper introduces a unified analytical approach for chaos synchronization in generalized Lorenz systems using linear state error feedback, providing optimized criteria applicable to various chaotic systems.

Contribution

It develops a rigorous synchronization criterion based on linearization and Lyapunov methods, and derives optimized algebraic conditions for multiple generalized Lorenz systems.

Findings

Derived synchronization conditions for classical Lorenz, Chen, Lv, and unified systems.

Optimized criteria show improved sharpness over existing methods.

Numerical validation confirms effectiveness of the proposed synchronization scheme.

Abstract

This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state error variables. A sufficient synchronization criterion for a general linear state error feedback controller is rigorously proven by means of linearization and Lyapunov's direct methods. When a simple linear controller is used in the scheme, some easily implemented algebraic synchronization conditions are derived based on the upper and lower bounds of the master chaotic system. These criteria are further optimized to improve their sharpness. The optimized criteria are then applied to four typical generalized Lorenz systems, i.e. the classical Lorenz system, the Chen system, the Lv system and a unified chaotic system, obtaining precise corresponding synchronization conditions. The advantages of the new criteria are revealed by analytically and numerically comparing their sharpness with that of the known criteria existing in the literature.