Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System

Abstract

Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. In this paper, we introduce a three-dimensional fractional-order chaotic system. The important finding by analysis is that the position of signal x3 descends at the speed of 1/c as the parameter b increases, and the signal amplitude of x1, x2 can be controlled by the parameter m in terms of the power function with the index −1/2. What is more, the dynamics remains constant with the variation of parameters b and m. Consequently, this system can provide rich encoding keys for chaotic communication. By considering the properties of amplitude and position modulation, the partial projective synchronization and partial phase synchronization are realized with linear control scheme. The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller. Numerical simulations are executed to confirm the theoretical analysis.