scholarly journals Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

2017 ◽  
Vol 7 (6) ◽  
pp. 3446 ◽  
Author(s):  
Hamed Tirandaz ◽  
Mohsen Ahmadnia ◽  
Hamid Reza Tavakoli
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Synchronization Problem ◽  
Projective Lag Synchronization ◽  
Control And Synchronization

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

2018 ◽  
Vol 7 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Hamed Tirandaz
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Parameters Estimation ◽  
Control Law ◽  
Complete Control ◽  
Synchronization Problem ◽  
Control And Synchronization ◽  
Adaptive Control Law

Abstract Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Switched Projective Synchronization of the Stochastic Newton-Leipnik System

2013 ◽  
Vol 328 ◽  
pp. 570-574
Author(s):  
Duan Dong ◽  
Shao Juan Ma ◽  
Jie Zheng
Keyword(s):  
Hilbert Spaces ◽  
Chaotic Systems ◽  
Control Method ◽  
Random Parameter ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Deterministic System ◽  
Lyapunov Stability Theorem ◽  
Orthogonal Polynomial Expansion

The paper is involved with switched projective synchronization of two identical chaotic systems with random parameter using adaptive control method. Based on the orthogonal polynomial expansion of the Hilbert spaces, the Newton-Leipnik system with random parameter is transformed as the equivalent deterministic system. At last, an adaptive controller can be designed by the Lyapunov stability theorem for achieving switched projective synchronization of the equivalent deterministic system with different initial values. Corresponding numerical simulations are performed to verify the effectiveness of presented schemes for synchronizing the stochastic Newton-Leipnik system.

Anti-Synchronization for a Modified Chen-Qi-Like Chaotic System

2012 ◽  
Vol 220-223 ◽  
pp. 2113-2116
Author(s):  
Su Hai Huang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Stability Theorem ◽  
Control Law ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Dynamical Characteristics ◽  
Control Scheme ◽  
Adaptive Control Scheme

A modified Chen-Qi-like chaotic system is presented. Some basic dynamical characteristics of this system are studied by calculating the Lyapunov exponent and phase figure. Based on the Lyapunov stability theorem, adaptive control scheme and parameters update law are presented for the anti-synchronization of new chaotic systems with fully unknown parameters. Finally, the numerical simulation verify that the control law and parameter changing are correct.

Projective lag synchronization in drive-response dynamical networks

2014 ◽  
Vol 25 (11) ◽  
pp. 1450068 ◽  
Author(s):  
Ghada Al-Mahbashi ◽  
Mohd Salmi Md Noorani ◽  
Sakhinah Abu Bakar
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
Feedback Control Method ◽  
Projective Lag Synchronization ◽  
Error Dynamics ◽  
The Stability

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

scholarly journals Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xiuli Chai ◽  
Zhihua Gan ◽  
Chunxiao Shi
Keyword(s):  
Dynamical Systems ◽  
Chaotic System ◽  
Control Method ◽  
General Theorem ◽  
Three Dimensional ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Lag Synchronization ◽  
Projective Lag Synchronization ◽  
Hyperchaotic Systems

Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive control method. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

scholarly journals Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

2017 ◽  
Vol 7 (6) ◽  
pp. 3436
Author(s):  
Hamed Tirandaz ◽  
Mohsen Ahmadnia ◽  
Hamid Reza Tavakoli
Keyword(s):  
Nonlinear Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Adaptive Methods ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Synchronization Problem ◽  
Modified Projective Synchronization ◽  
Nonlinear Control Method ◽  
Speed And Accuracy

<p>The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views.</p>

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

2021 ◽  
pp. 107754632110264
Author(s):  
Cun-Fang Feng ◽  
Hai-Jun Yang ◽  
Cai Zhou
Keyword(s):  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Lag Synchronization ◽  
Different Dimensions ◽  
Projective Lag Synchronization ◽  
General Method

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Synchronization of Liu-Su-Liu and Liu-Chen-Liu Chaotic Systems by Nonlinear Feedback Control

2019 ◽  
Vol 16 (12) ◽  
pp. 4903-4907
Author(s):  
Regan Murugesan ◽  
Suresh Rasappan ◽  
Pugalarasu Rajan ◽  
Sathish Kumar Kumaravel
Keyword(s):  
Feedback Control ◽  
Nonlinear Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Nonlinear Control Method ◽  
Different Chaotic Systems

This paper investigates the global chaos synchronization of identical Liu-Su-Liu chaotic systems (2006) and non-identical Liu-Su-Liu chaotic system (2006) and Liu-Chen-Liu chaotic system (2007). In this paper, active nonlinear control method has been successfully applied to synchronize two identical Liu-Su-Liu chaotic systems and then to synchronize two different chaotic systems, viz. Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to synchronize Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Numerical simulations are also given to illustrate the proposed synchronization approach.

scholarly journals Adaptive Integral Observer-Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiuchun Li ◽  
Jianhua Gu ◽  
Wei Xu
Keyword(s):  
Neural Network ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Original System ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
External Perturbations ◽  
Response Systems ◽  
Barbalat Lemma

Considering the effects of external perturbations on the state vector and the output of the original system, this paper proposes a new adaptive integral observer method to deal with chaos synchronization between the drive and response systems with unknown parameters. The analysis and proof are given by means of the Lyapunov stability theorem and Barbalat lemma. This approach has fewer constraints because many parameters related to chaotic system can be unknown, as shown in the paper. Numerical simulations are performed in the end and the results show that the proposed method is not only suitable to the representative chaotic systems but also applied to some neural network chaotic systems.

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