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

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

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.

scholarly journals Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft

1996 ◽  
Vol 2 (4) ◽  
pp. 277-299 ◽  
Author(s):  
Xinzhi Liu ◽  
Allan R. Willms
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Necessary And Sufficient

Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete-time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

scholarly journals Robust Controller Design for Modified Projective Synchronization of Chen-Lee Chaotic Systems with Nonlinear Inputs

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Jui-sheng Lin ◽  
Neng-Sheng Pai ◽  
Her-Terng Yau
Keyword(s):  
Chaotic Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Variable Structure ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Nonlinear Controller ◽  
Input Nonlinearity ◽  
Structure Control ◽  
Modified Projective Synchronization

This study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchronization, antisynchronization, and projective synchronization in spite of the input nonlinearity. The numerical simulation results show that the synchronization and antisynchronization can coexist in Chen-Lee chaotic systems. It demonstrates the validity and feasibility of the proposed controller.

A New Generalized-Type of Synchronization for Discrete-Time Chaotic Dynamical Systems

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Discrete Time ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Effective Control ◽  
Nonlinear Controllers ◽  
Control Schemes ◽  
New Type ◽  
Different Dimensions ◽  
Generalized Type

In this paper, a new type of chaos synchronization in discrete-time is proposed by combining matrix projective synchronization (MPS) and generalized synchronization (GS). This new chaos synchronization type allows us to study synchronization between different dimensional discrete-time chaotic systems in different dimensions. Based on nonlinear controllers and Lyapunov stability theory, effective control schemes are introduced and new synchronization criterions are derived. Numerical simulations are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

Dual Combination Synchronization of Six Chaotic Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Junwei Sun ◽  
Suxia Jiang ◽  
Guangzhao Cui ◽  
Yanfeng Wang
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Combination Synchronization

Based on combination synchronization of three chaotic systems and combination–combination synchronization of four chaotic systems, a novel scheme of dual combination synchronization is investigated for six chaotic systems in the paper. Using combined adaptive control and Lyapunov stability theory of chaotic systems, some sufficient conditions are attained to realize dual combination synchronization of six chaotic systems. The corresponding theoretical proofs and numerical simulations are presented to demonstrate the effectiveness and correctness of the dual combination synchronization. Due to the complexity of dual combination synchronization, it will be more secure and interesting to transmit and receive signals in application of communication.

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

2011 ◽  
Vol 22 (11) ◽  
pp. 1281-1291 ◽  
Author(s):  
RANCHAO WU ◽  
DONGXU CAO
Keyword(s):  
Numerical Simulation ◽  
Dynamical Systems ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Simulation Results ◽  
Invariant Principle

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.

scholarly journals Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE IDENTICAL AND DIFFERENT CYQY HYPER-CHAOTIC SYSTEMS

2014 ◽  
Vol 28 (04) ◽  
pp. 1450013 ◽  
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
NA WEI ◽  
SI-HUI JIANG ◽  
XIU-KUN WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper further investigates the adaptive full state hybrid projective synchronization (FSHPS) of hyper-chaotic systems — CYQY system with fully unknown parameters and perturbations. Based on the Lyapunov stability theory, adaptive controllers and updating laws of parameters can be designed for achieving the FSHPS of the CYQY hyper-chaotic systems with the same and different structures. Two groups numerical simulations are provided to verify the effectiveness of the proposed scheme.

scholarly journals Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

2018 ◽  
Vol 23 (4) ◽  
pp. 583-598 ◽  
Author(s):  
Ahlem Gasri ◽  
Adel Ouannas ◽  
Kayode S. Ojo ◽  
Viet-Thanh Pham
Keyword(s):  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Generalized Synchronization ◽  
Continuous Time Systems ◽  
New Type ◽  
Inverse Generalized Synchronization ◽  
Time Systems ◽  
Hyperchaotic Systems

In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3D master chaotic system and 4D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein.

scholarly journals Anti-synchronization in different new chaotic systems via active nonlinear control

2013 ◽  
Vol 23 (2) ◽  
pp. 229-242
Author(s):  
Ayub Khan ◽  
Ram Pravesh Prasad
Keyword(s):  
Nonlinear Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory

In this paper, we discuss anti-synchronization between two identical new chaotic systems and anti-synchronization between another two identical new chaotic systems by active nonlinear control. The sufficient conditions for achieving the anti-synchronization of two new chaotic systems are derived based on Lyapunov stability theory. Numerical simulations are provided for illustration and verification of the proposed method.

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