The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non-identical Dimensions and Orders.

Samir Bendoukha,Viet-Thanh Pham,Adel Ouannas,Amina-Aicha Khennaoui,Van Van Huynh,Giuseppe Grassi,Xiong Wang

doi:10.3390/e20090710

Abstract

This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.

Highlights

Discrete-time chaotic systems have been the center of attention in the fields of control [1,2] and secure communications in the last few years [3,4,5,6]
Where t ∈ Na+1−υ, 0 < υ ≤ 1, f i : R2 −→ R, 1 ≤ i ≤ 2, bij ∈ R3×3 is the linear part of the drive system, gi : R3 −→ R, 1 ≤ i ≤ 3, are nonlinear functions, and ui, i = 1, 2, 3, are controllers to be designed
Based on Definition 1, we may define the co-existence of projective synchronization (PS), full state hybrid projective synchronization (FSHPS) and generalized synchronization (GS) for the coupled systems (5) and (6) as follows

Summary

Introduction

Discrete-time chaotic systems have been the center of attention in the fields of control [1,2] and secure communications in the last few years [3,4,5,6]. The chaotic nature of the dynamical systems, which seems random-like but is completely determined and can be predicted once the initial conditions are known. This allows for the generation of pseudo–random sequences in secret or private-key encryption. Among the well known discrete-time chaotic systems proposed throughout the years are the Hénon map [7], the Lozi system [8], the generalized Hénon map [9] and the Baier–Klein system [10]

Results

Discussion

Conclusion