Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters

Abstract

The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

“…However, quite limited results on fractional order complex chaotic systems have been reported so far, due to the complexity of the problem and the ambiguity of the application field. Still, some scholars have tried and put forward some synchronization methods: adaptive synchronization (Tian, 2014), modified projective synchronization (Yang and Jiang, 2015), and active synchronization (Singh et al., 2017). At present, there are two ways to study complex chaotic systems and fractional order complex chaotic systems.…”