Rate Estimation of Identical Synchronization by Designing Controllers

Abstract

This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system.

Chaos control in Shimizu Morioka system by Lie algebraic exact linearization

“…Shimizu-Morioka dynamical system is a chaotic [10,12] system that is algebraically simpler than the Lorentz system but produces qualitatively the same dynamics as Lorentz system in its chaotic regime. The Shimizu Morioka non-linear dynamical system is given by:…”