Difference synchronization in nonidentical discrete-time chaotic systems with different dimensions using three scaling matrices

Abstract

In this paper, we consider the difference synchronization for different chaotic maps with different dimensions using three scaling matrices. The proposed method allows us to study difference synchronization of two master discrete-time chaotic systems with dimension n and one response discrete-time chaotic system with dimension m . Based on the Lyapunov stability theory and stability property of linear discrete-time systems, controllers are derived to achieve the difference synchronization among three nonidentical discrete-time chaotic systems with different dimensions in two cases: n < m and n > m . For the case n < m , 2D Fold map and 2D Hénon map are used as the master systems, and the 3D Hitzl-Zele map is chosen as the slave system to simulate the difference synchronization. For the case n > m , 3D Stefanski map and 3D Baier-Klein map are adopted as the master systems, and 2D Lorenz discrete-time chaotic system is used as the slave system during the simulation. The numerical simulations illustrate the effectiveness and feasibility of the proposed method.