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.

scholarly journals New type of chaos synchronization in discrete-time systems: the F-M synchronization

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 174-182 ◽  
Author(s):  
Adel Ouannas ◽  
Giuseppe Grassi ◽  
Abdulrahman Karouma ◽  
Toufik Ziar ◽  
Xiong Wang ◽  
...  
Keyword(s):  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
The Novel ◽  
Synchronization Index ◽  
Nonlinear Controllers ◽  
The Matrix ◽  
New Type ◽  
Different Dimensions ◽  
Inverse Generalized Synchronization ◽  
Time Systems

AbstractIn this paper, a new type of synchronization for chaotic (hyperchaotic) maps with different dimensions is proposed. The novel scheme is called F – M synchronization, since it combines the inverse generalized synchronization (based on a functional relationship F) with the matrix projective synchronization (based on a matrix M). In particular, the proposed approach enables F – M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F – M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein.

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.

Improved Control Schemes for Projective Synchronization of Delayed Neural Networks with Unmatched Coefficients

2019 ◽  
Vol 34 (03) ◽  
pp. 2051005 ◽  
Author(s):  
Abdujelil Abdurahman ◽  
Haijun Jiang
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Chaos Synchronization ◽  
Projective Synchronization ◽  
Chaotic Neural Networks ◽  
Delayed Neural Networks ◽  
Mixed Time Delays ◽  
Control Schemes ◽  
Master System ◽  
Inequality Techniques

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper.

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 Adaptive Synchronization for Hyperchaotic Liu System

2022 ◽  
Vol 9 ◽  
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Gang Zheng
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Control Schemes ◽  
Liu System ◽  
Adaptive Control Law

In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.

scholarly journals Projective Synchronization of Chaotic Systems Via Backstepping Design

2013 ◽  
Vol 18 (3) ◽  
pp. 965-973 ◽  
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

scholarly journals Projective synchronization for 4D hyperchaotic system based on adaptive nonlinear control strategy

2020 ◽  
Vol 19 (2) ◽  
pp. 715 ◽  
Author(s):  
Zaidoon Sh. Al-Talib ◽  
Saad Fawzi AL-Azzawi
Keyword(s):  
Nonlinear Control ◽  
Control Strategy ◽  
Chaotic Oscillation ◽  
Positive Definite Matrix ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Nonlinear Controller ◽  
Unknown Parameters ◽  
Nonlinear Controllers

<span>The main purpose of the paper is to projective synchronous chaotic oscillation in the real four-dimensional hyperchaotic model via designing many adaptive nonlinear controllers. Firstly, in view that there are many strategies in the design process of existing controllers, a nonlinear control strategy is considered as one of the important powerful tools for controlling the dynamical systems. The prominent advantage of the nonlinear controller lies in that it deals with known and unknown parameters. Then, the projective synchronize behavior of a four-dimensional hyperchaotic system is analyzed by using the Lyapunov stability theory and positive definite matrix, and the nonlinear control strategy is adopted to synchronize the hyperchaotic system. Finally, the effectiveness and robustness of the designed adaptive nonlinear controller are verified by simulation.</span>

scholarly journals Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 942-949 ◽  
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Amina–Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Xiong Wang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Strategies ◽  
Response System ◽  
Discrete Time Systems ◽  
Different Dimensions ◽  
Synchronization Scheme ◽  
Time Systems

Abstract In this paper, we study the synchronization of fractional–order discrete–time chaotic systems by means of two scaling matrices Θ and Φ. The considered synchronization scheme can be tailored to encompass several types of classical synchronization types. We proposed two nonlinear control strategies for the Θ–Φ synchronization of an m–dimensional drive system and an n–dimensional response system, whereby the synchronization dimension d = m and d = n, respectively. Numerical examples are presented to test the findings of the study.

scholarly journals A Novel Scheme Adaptive Hybrid Dislocated Synchronization for Two Identical and Different Memristor Chaotic Oscillator Systems with Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jie Chen ◽  
Junwei Sun ◽  
Ming Chi ◽  
Xin-Ming Cheng
Keyword(s):  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Parameters Estimation ◽  
Drive System ◽  
Projective Synchronization ◽  
Chaotic Oscillator ◽  
Uncertain Parameters ◽  
State Variables ◽  
Response System

The drive system can synchronize with the response system by the scaling factor in the traditional projective synchronization. This paper proposes a novel adaptive hybrid dislocated synchronization with uncertain parameters scheme for chaos synchronization using the Lyapunov stability theory. The drive system is synchronized by the sum of hybrid dislocated state variables for the response system. By designing effective hybrid dislocated adaptive controller and hybrid dislocated adaptive law of the parameters estimation, we investigate the synchronization of two identical memristor chaotic oscillator systems and two different memristor chaotic oscillator systems with uncertain parameters. Finally, the numerical simulation examples are provided to show the effectiveness of our method.

scholarly journals Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Adel Ouannas ◽  
Xiong Wang ◽  
Viet-Thanh Pham ◽  
Toufik Ziar
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Effective Control ◽  
Lyapunov Approach ◽  
Integer Order ◽  
Fractional Order Differential Equations ◽  
Control Schemes ◽  
Stability Method ◽  
Different Dimensions ◽  
Theoretical Results

We present new approaches to synchronize different dimensional master and slave systems described by integer order and fractional order differential equations. Based on fractional order Lyapunov approach and integer order Lyapunov stability method, effective control schemes to rigorously study the coexistence of some synchronization types between integer order and fractional order chaotic systems with different dimensions are introduced. Numerical examples are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

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