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

Abstract EN

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.