A Novel Mathematical Analysis for Predicting Master-Slave Chaotic Synchronization

Abstract

In this chapter, a novel mathematical analysis for predicting master-slave chaotic synchronization is presented. In most situations when examining this type of synchronization one considers the asymptotic stability of the particular system via Lyapunov’s direct method, or conditional Lyapunov exponents are considered. Initially, in this chapter, Lyapunov’s direct method is used to show the asymptotic stability within the simplest piecewise linear master-slave chaotic flow. However, primarily the master-slave synchronization properties of the simplest quadratic chaotic flow and Ueda chaotic system are examined directly by means of mathematical manipulation of their dynamical equations, where possible, as well as via numerical simulations. In order to achieve this, numerical simulations and theoretical analysis are made use of in conjunction. In this way, it is shown that the synchronization error of the two aforementioned chaotic master-slave systems can indeed be predicted for certain driving signals, without the need for either analytical or numerical evaluation of the conditional Lyapunov exponents or employment of Lyapunov’s direct method.