FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA NONLINEAR ADAPTIVE–IMPULSIVE CONTROL

In this paper, function projective synchronization of chaotic systems is investigated through nonlinear adaptive–impulsive control. To achieve synchronization, suitable nonlinear continuous and impulsive controllers are designed, according to invariant principle of impulsive dynamical systems. Sufficient conditions are given to ensure the synchronization. Numerical simulation results show the effectiveness of the proposed scheme.

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THE HYBRID FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS

International Journal of Modern Physics C ◽

10.1142/s0129183109013972 ◽

2009 ◽

Vol 20 (05) ◽

pp. 789-797

Author(s):

YONG-GUANG YU ◽

HAN-XIONG LI ◽

JUN-ZHI YU

Keyword(s):

Numerical Simulation ◽

Lyapunov Stability ◽

Chaotic Systems ◽

Lyapunov Stability Theory ◽

Adaptive Controller ◽

Projective Synchronization ◽

Function Projective Synchronization ◽

Hybrid Function ◽

Simulation Results ◽

Different Chaotic Systems

This paper mainly investigated a hybrid function projective synchronization of two different chaotic systems. Based on the Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is designed. This technique is applied to achieve the synchronization between Lorenz and Rössler chaotic systems, and the synchronization of hyperchaotic Rössler and Chen systems. The numerical simulation results illustrate the effectiveness and feasibility of the proposed scheme.

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Projective Synchronization of Chaotic Systems Via Backstepping Design

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2013-0060 ◽

2013 ◽

Vol 18 (3) ◽

pp. 965-973 ◽

Cited By ~ 1

Author(s):

A. Tarai ◽

M.A. Khan

Keyword(s):

Numerical Simulation ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Lyapunov Stability Theory ◽

Discrete Dynamical Systems ◽

Projective Synchronization ◽

Control Law ◽

Backstepping Design ◽

Simulation Results ◽

Duffing Map

Abstract Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm

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Generalized Projective Synchronization for a Class of Continuous Chaotic Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.50-51.258 ◽

2011 ◽

Vol 50-51 ◽

pp. 258-261

Author(s):

Ya Fei Zhou ◽

Dong Zhang

Keyword(s):

Numerical Simulation ◽

Chaotic Systems ◽

Mathematical Proof ◽

Construction Method ◽

Projective Synchronization ◽

Response System ◽

Simulation Results ◽

Generalized Projective Synchronization

In this paper, a generalized projective synchronization (GPS) scheme for a class of continuous chaotic systems is investigated by using only one sate variable and its time derivatives. The construction method of response system is proposed. The mathematical proof of the GPS scheme is provided. The synchronization technique is simple and theoretically rigorous. Finally, the corresponding numerical simulation results demonstrate the effectiveness of the proposed schemes.

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Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

Mathematical Problems in Engineering ◽

10.1155/2013/751616 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 9

Author(s):

Xiuli Chai ◽

Zhihua Gan ◽

Chunxiao Shi

Keyword(s):

Dynamical Systems ◽

Impulsive Control ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Upper Bounds ◽

Hyperchaotic System ◽

Impulsive Synchronization ◽

Control Scheme ◽

Functional Differential ◽

Invariant Principle

The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustrate the effectiveness and feasibility of the proposed methods.

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On Matrix Projective Synchronization and Inverse Matrix Projective Synchronization for Different and Identical Dimensional Discrete-Time Chaotic Systems

Journal of Chaos ◽

10.1155/2016/4912520 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7 ◽

Cited By ~ 7

Author(s):

Adel Ouannas ◽

Raghib Abu-Saris

Keyword(s):

Dynamical Systems ◽

Discrete Time ◽

Stability Theory ◽

Chaotic Systems ◽

Sufficient Conditions ◽

Lyapunov Stability Theory ◽

Inverse Matrix ◽

Projective Synchronization ◽

Linear Dynamical Systems ◽

New Type

The problem of matrix projective synchronization (MPS) in discrete-time chaotic systems is investigated, and a new type of discrete chaos synchronization called inverse matrix projective synchronization (IMPS) is introduced. Sufficient conditions are derived for achieving MPS and IMPS between chaotic dynamical systems in discrete-time of different and identical dimensions. Based on new control schemes, Lyapunov stability theory, and stability theory of linear dynamical systems in discrete-time, some synchronization criteria are obtained. Numerical examples and simulations are used to illustrate the use of the proposed schemes.

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