scholarly journals Lag Synchronization of Hyperchaotic Systems via Intermittent Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Wei Zhang ◽  
Pengcheng Wei ◽  
Qi Han
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Lag Synchronization ◽  
Control Scheme ◽  
Hyperchaotic Systems ◽  
Theoretical Results

Different from the most existing results, in this paper an intermittent control scheme is designed to achieve lag synchronization of coupled hyperchaotic systems. Several sufficient conditions ensuring lag synchronization are proposed by rigorous theoretical analysis with the help of the Lyapunov stability theory. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

2008 ◽  
Vol 15 (04) ◽  
pp. 371-382 ◽  
Author(s):  
M. M. Al-sawalha ◽  
M. S. M. Noorani
Keyword(s):  
Theoretical Analysis ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
High Dimensional ◽  
Analysis Strategy ◽  
Relevant Variables ◽  
Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

scholarly journals Anti-Synchronization of Fractional-Order Chaotic Circuit with Memristor via Periodic Intermittent Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Chaotic Circuit ◽  
Control Scheme

In this paper, the anti-synchronization of fractional-order chaotic circuit with memristor (FCCM) is investigated via a periodic intermittent control scheme. Based on the principle of periodic intermittent control and the Lyapunov stability theory, a novel criterion is adopted to realize the anti-synchronization of FCCM. Finally, some examples of numerical simulations are exploited to verify the feasibility of theoretical analysis.

scholarly journals Synchronization of Coupled Networks with Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Yi Zuo ◽  
Xinsong Yang
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Nonlinear Perturbations ◽  
Coupled Networks ◽  
Barbalat Lemma ◽  
Asymptotic Synchronization ◽  
Theoretical Results

Asymptotic synchronization for a class of coupled networks with nondelayed and delayed couplings is investigated. A distinct feature of the network is that all the dynamical nodes are affected by uncertain nonlinear nonidentical perturbations. In order to synchronize the network onto a given isolate trajectory, a novel adaptive controller is designed to overcome the effects of the nonidentical uncertain nonlinear perturbations. The designed controller has better robustness than classical adaptive controller, since it can realize the synchronization goal whether the nodes have these perturbations or not. Based on the Lyapunov stability theory and the Barbalat lemma, sufficient conditions guaranteeing the asymptotic synchronization of the coupled network are derived. Two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results. Simulations also demonstrate that our adaptive controller has better robustness than existing ones.

scholarly journals Intermittent Control for Cluster-Delay Synchronization in Directed Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jianbao Zhang ◽  
Yi Wang ◽  
Zhongjun Ma ◽  
Jianlong Qiu ◽  
Fawaz Alsaadi
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Recent Literature ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Directed Network ◽  
Intermittent Control ◽  
Numerical Examples ◽  
Control Protocol ◽  
Control Schemes

We investigate cluster-delay synchronization of a directed network possessing cluster structures by designing an intermittent control protocol. Based on Lyapunov stability theory, we proved that synchronization can be realized for oscillators in the same cluster and cluster-delay synchronization can be realized for the whole network. By simplifying the obtained sufficient conditions, we carry out a succinct and utilitarian corollary. In addition, comparative researches are carried out to show the differences and the usefulness of the obtained results with respect to other similar controllers from the recent literature. Finally we provide two numerical examples to show the effectiveness of the control schemes.

scholarly journals Pinning synchronization of the drive and response dynamical networks with lag

2014 ◽  
Vol 24 (3) ◽  
pp. 257-270 ◽  
Author(s):  
Bohui Wen ◽  
Mo Zhao ◽  
Fanyu Meng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Schur Complement ◽  
Pinning Control ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
General Complex ◽  
Minimum Number

Abstract This paper investigates the pinning synchronization of two general complex dynamical networks with lag. The coupling configuration matrices in the two networks are not need to be symmetric or irreducible. Several convenient and useful criteria for lag synchronization are obtained based on the lemma of Schur complement and the Lyapunov stability theory. Especially, the minimum number of controllers in pinning control can be easily obtained. At last, numerical simulations are provided to verify the effectiveness of the criteria

scholarly journals Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

2021 ◽  
Vol 54 (5) ◽  
pp. 789-795
Author(s):  
Yamina Haddadji ◽  
Mohamed Naguib Harmas ◽  
Abdlouahab Bouafia ◽  
Ziyad Bouchama
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Simulation Results ◽  
Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

scholarly journals Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Qing Wang ◽  
Yongguang Yu ◽  
Hu Wang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Convergence Speed ◽  
External Disturbances ◽  
Adaptive Controllers ◽  
Robust Synchronization ◽  
Hyperchaotic Systems

The robust synchronization of hyperchaotic systems with uncertainties and external disturbances is investigated. Based on the Lyapunov stability theory, the appropriate adaptive controllers and parameter update laws are designed to achieve the synchronization of uncertain hyperchaotic systems. The robust synchronization of two hyperchaotic Chen systems is taken as an example to verify the feasibility of the presented schemes. The size of the subcontroller gain’s influences on the convergence speed is discussed. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed synchronization schemes.

scholarly journals Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 304-313 ◽  
Author(s):  
M. Mossa Al-Sawalha ◽  
Ayman Al-Sawalha
Keyword(s):  
Adaptive Control ◽  
Dynamical Systems ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Laws ◽  
Analytic Expression ◽  
Hyperchaotic Systems

AbstractThe objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.

scholarly journals Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Weiping Wang ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Jialiang Yuan ◽  
Jinghua Xiao ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Real World ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Definition Of ◽  
First Time ◽  
Theoretical Results

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.

IMPULSIVE SYNCHRONIZATION OF HYPERCHAOTIC LÜ SYSTEM

2011 ◽  
Vol 25 (27) ◽  
pp. 3671-3678 ◽  
Author(s):  
XING-YUAN WANG ◽  
MING-JUN WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Impulsive Synchronization ◽  
Lü System ◽  
Feedback Strength ◽  
Hyperchaotic Lu System ◽  
Lu System

In this paper, the impulsive synchronization of hyperchaotic Lü systems is discussed. The sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. The method is proved true by Lyapunov stability theory. In addition, a scheme of impulsive synchronization via transmitting single signal is presented. Numerical simulations show the effectiveness of the methods.

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