On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

Adel Ouannas

doi:10.1155/2014/983293

Abstract

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

Highlights

Many mathematical models of biological processes, physical processes, and chemical processes, etc., were dened using chaotic dynamical systems in discrete-time
By the same procedure we can define a new type of synchronization, called inverse fullstate hybrid projective synchronization (IFSHPS), when each drive system state synchronizes with a linear combination of response system states
In this paper, based on nonlinear control method in 2D and discrete-time Lyapunov stability theory, firstly, a new synchronization controller is designed for full-state hybrid projective synchronization (FSHPS) of general chaotic systems

Summary

Introduction

Many mathematical models of biological processes, physical processes, and chemical processes, etc., were dened using chaotic dynamical systems in discrete-time. By the same procedure we can define a new type of synchronization, called inverse fullstate hybrid projective synchronization (IFSHPS), when each drive system state synchronizes with a linear combination of response system states. In this paper, based on nonlinear control method in 2D and discrete-time Lyapunov stability theory, firstly, a new synchronization controller is designed for full-state hybrid projective synchronization (FSHPS) of general chaotic systems. A new control scheme is proposed to study the problem of inverse full-state hybrid projective synchronization (IFSHPS) for arbitrary chaotic systems. In order to show the effectiveness of the proposed synchronization schemes, our approach is applied to the drive Fold discretetime system and the controlled Lorenz discrete-time system to achieve FSHPS and IFSHPS, respectively.

Definitions of FSHPS and IFSHPS

Controller Design for FSHPS in 2D

New Criterion for IFSHPS in 2D

Numerical Application and Simulations

Conclusion