Λ − φ generalized synchronization: application to fractional hyperchaotic systems with arbitrary dimensions and orders

Abstract

This paper investigates the $\Lambda -\phi $ generalized synchronization between non-identical fractional-order systems characterized by different dimensions and different orders. The $\Lambda -\phi $ generalized synchronization combines the inverse matrix projective synchronization with the generalized synchronization. In particular, the proposed approach enables $\Lambda -\phi $ generalized synchronization to be achieved between n-dimensional master system and m-dimensional slave system in different dimensions. The technique, which exploits nonlinear controllers, stability property of integer-order linear systems and Lyapunov stability theory, proves to be effective in achieving the $\Lambda -\phi $ generalized synchronization. Finally, the approach is applied between 4-D and 5-D fractional hyperchaotic systems with the aim to illustrate the capabilities of the novel scheme proposed herein.

Keywords

• chaos
• inverse matrix projective synchronization
• generalized synchronization
• lyapunov stability theory
• fractional hyperchaotic systems