Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices

Abstract

In this paper, we study the synchronization of fractional–order discrete–time chaotic systems by means of two scaling matrices Θ and Φ. The considered synchronization scheme can be tailored to encompass several types of classical synchronization types. We proposed two nonlinear control strategies for the Θ–Φ synchronization of an m–dimensional drive system and an n–dimensional response system, whereby the synchronization dimension d = m and d = n, respectively. Numerical examples are presented to test the findings of the study.

Keywords

• chaotic maps
• discrete-time fractional calculus, synchronization
• different dimensions
• linear systems
• stability
• 34a08
• 34h10
• 34d06