scholarly journals Hybrid Synchronization Problem of a Class of Chaotic Systems by an Universal Control Method

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 552 ◽  
Author(s):  
Zuoxun Wang ◽  
Rongwei Guo
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Algebraic Equations ◽  
Synchronization Problem ◽  
Universal Control ◽  
All Solutions ◽  
Nonlinear Algebraic Equations ◽  
Hybrid Synchronization ◽  
Necessary And Sufficient ◽  
Synchronization Problems

The hybrid synchronization problem of a class of chaotic systems is investigated in this paper. Firstly, the existence of hybrid synchronization problems in such systems is proved theoretically by a proposed necessary and sufficient condition. That is, the hybrid synchronization problem is equivalent to solve a group of nonlinear algebraic equations about α . It is interesting that one value of α indicates one type of synchronization. Secondly, all solutions for the hybrid synchronization problem are obtained by finding solutions of all the above equations about α . Thirdly, an universal control method is proposed to realize such hybrid synchronization problems. Finally, illustrative examples are provided to verify the validity and effectiveness of the obtained results.

scholarly journals Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 718
Author(s):  
Runlong Peng ◽  
Cuimei Jiang ◽  
Rongwei Guo
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Dynamic Feedback ◽  
Synchronization Problem ◽  
Feedback Control Method ◽  
Single Input ◽  
Dynamic Feedback Control ◽  
Necessary And Sufficient

This paper investigates the partial anti-synchronization problem of fractional-order chaotic systems through the dynamic feedback control method. Firstly, a necessary and sufficient condition is proposed, by which the existence of the partial anti-synchronization problem is proved. Then, an algorithm is given and used to obtain all solutions of this problem. Moreover, the partial anti-synchronization problem of the fractional-order chaotic systems is realized through the dynamic feedback control method. It is noted that the designed controllers are single-input controllers. Finally, two illustrative examples with numerical simulations are used to verify the correctness and effectiveness of the proposed 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>

scholarly journals Simultaneity of Synchronization and Antisynchronization in a Class of Chaotic Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhi Liu ◽  
Rongwei Guo ◽  
Yi Qi ◽  
Cuimei Jiang
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Synchronization Phenomenon ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Theoretical Results

In this paper, a new synchronization phenomenon, that is, the simultaneity of synchronization and antisynchronization, is investigated for a class of chaotic systems. First, for a given chaotic system, necessary and sufficient conditions for the simultaneity of synchronization and antisynchronization are proved. Then, based on these conditions, all solutions of such synchronization phenomenon for a given chaotic system are derived. After that, physical controllers that are not only simple but also implementable are designed to realize the simultaneity of synchronization and antisynchronization in the above system. Finally, illustrative examples based on numerical simulations are used to verify the validity and effectiveness of the above theoretical results.

Complex Hybrid Synchronization in Drive-Response Complex-Variable Chaotic Systems

2012 ◽  
Vol 13 (7-8) ◽  
Author(s):  
Zhaoyan Wu
Keyword(s):  
Complex Variable ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Scheme ◽  
Hybrid Synchronization ◽  
Complex Hybrid ◽  
First Time ◽  
In Virtue Of ◽  
Response Complex

AbstractIn this paper, the concept of complex hybrid synchronization in complex-variable chaotic system is introduced for the first time. Based on Lyapunov stability theory, two typical complex-variable chaotic systems are considered and corresponding controllers are designed to achieve complex hybrid synchronization. Further, a universal control method in virtue of adaptive control scheme is proposed. Numerical examples are provided to show the effectiveness of the proposed method.

scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

PREDICTIVE CONTROL OF CONTINUOUS CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (02) ◽  
pp. 587-592 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
ABDELHAMID CHEBBAH ◽  
NOURA MANSOURI
Keyword(s):  
Predictive Control ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Delayed Feedback Control ◽  
System Sensitivity ◽  
Necessary And Sufficient ◽  
Time Systems

In this paper, a predictive control method is suggested for chaos control in continuous-time systems. This method combines the delayed feedback control of high order continuous-time chaotic systems with the prediction-based method of discrete-time chaotic systems. Moreover, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed method. Both control performance and system sensitivity to initial conditions of this approach are demonstrated by numerical simulations.

scholarly journals Two Types of Synchronization Problems in a New 5D Hyperchaotic System

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Bin Li ◽  
Xue Yang ◽  
Qixing Liang ◽  
Zhi Li
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Hyperchaotic System ◽  
Dynamic Feedback ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Theoretical Results ◽  
Synchronization Problems

This paper investigates the synchronization problem in a new 5D hyperchaotic system. Firstly, the existence of two types of synchronization problems in the new 5D hyperchaotic system is proved. Then, by the dynamic feedback control method, one complete synchronization problem and three coexistence of complete synchronization and antisynchronization problems in such system are realized. Finally, numerical simulations are used to verify the validity and effectiveness of the theoretical results.

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.

Adaptive Modified Projective Synchronization Between Genesio and Rossler Chaotic Systems with Uncertainties

2012 ◽  
Vol 546-547 ◽  
pp. 1040-1044 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Ji Fei Liu ◽  
Rui Pan
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Projective Synchronization ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Control Laws ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Modified Projective Synchronization ◽  
Different Chaotic Systems

The paper discusses the modified projective synchronization of two different chaotic systems by nonlinear control laws, considering the conditions of the master-slave systems with uncertain parameters, the synchronization problem between Genesio system and Rossler system has been investigated, adopting the adaptive control method, a sufficient condition is attainted for the modified projective synchronization between master and slave system, finally, The control performances are verified by the numerical examples.

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