scholarly journals Synchronization and Lag Synchronization of Hyperchaotic Memristor-Based Chua’s Circuits

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Hui Wang ◽  
Xin Wang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Chua’S Circuit ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Chua's Circuit ◽  
Initial Values ◽  
Theoretical Results

A memristor-based five-dimensional (5D) hyperchaotic Chua’s circuit is proposed. Based on the Lyapunov stability theorem, the controllers are designed to realize the synchronization and lag synchronization between the hyperchaotic memristor-based Chua’s circuits under different initial values, respectively. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

Synchronization and Anti-Synchronization of the Chaotic Modified Chua's Circuits via a Same Controller

2012 ◽  
Vol 605-607 ◽  
pp. 1972-1975
Author(s):  
Jian Cai Leng ◽  
Rong Wei Guo
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Global Synchronization ◽  
Single Input ◽  
Theoretical Results

Based on the Lyapunov stability theorem, a same controller in the form is designed to achieve the global synchronization and anti-synchronization of the chaotic modified Chua's circuits. The controller obtained in this paper is simpler than those obtained in the existing results, and it is a linear single input controller. Numerical simulations verify the correctness and the effectiveness of the proposed theoretical results

Application of Synchronization Control Method to Zagzag System

2012 ◽  
Vol 241-244 ◽  
pp. 1067-1070
Author(s):  
Yin Li ◽  
Chun Long Zheng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Control Method ◽  
Stability Theorem ◽  
Synchronization Control ◽  
Lyapunov Stability Theorem ◽  
Synchronization Scheme

In this paper, synchronization control method of Zagzag system is discussed both theoretically and numerically. Based on the Lyapunov stability theorem and the chaotic methods, synchronization control is given and illustrated with Zagzag system as example. Numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization scheme.

GENERALIZED PROJECTIVE SYNCHRONIZATION OF A CLASS OF DELAYED NEURAL NETWORKS

2008 ◽  
Vol 22 (03) ◽  
pp. 181-190 ◽  
Author(s):  
JUAN MENG ◽  
XINGYUAN WANG
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Generalized Projective Synchronization

In this paper, the generalized projective synchronization of a class of delayed neural networks is investigated. Based on the Lyapunov stability theorem, a kind of controller is designed. The generalized projective synchronization of delayed neural networks can be achieved by using this kind of controller. Theoretical analysis and numerical simulations are provided to verify the feasibility and effectiveness of the proposed scheme.

SET STABILIZATION OF A MODIFIED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (02) ◽  
pp. 567-604 ◽  
Author(s):  
SHIHUA LI ◽  
YU-PING TIAN
Keyword(s):  
Equilibrium Point ◽  
Lyapunov Stability ◽  
Closed Loop ◽  
Invariant Set ◽  
Linear Feedback ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Linear Feedback Controller ◽  
Simulation Results ◽  
First Time

In this paper, we develop a simple linear feedback controller, which employs only one of the states of the system, to stabilize the modified Chua's circuit to an invariant set which consists of its nontrivial equilibria. Moreover, we show for the first time that the closed loop modified Chua's circuit satisfies set stability which can be considered as a generalization of common Lyapunov stability of an equilibrium point. Simulation results are presented to verify our method.

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

CONTROL OF n-SCROLL CHUA'S CIRCUIT

2009 ◽  
Vol 19 (11) ◽  
pp. 3813-3822 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
BILEL SAYOUD ◽  
HAMZA BOUMAIZA ◽  
NOURA MANSOURI
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Predictive Control ◽  
Control Method ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

STRANGE ATTRACTORS IN PERIODICALLY KICKED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (01) ◽  
pp. 83-98 ◽  
Author(s):  
QIUDONG WANG ◽  
ALI OKSASOGLU
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Strange Attractors ◽  
External Forcing ◽  
Chua’S Circuit ◽  
New Developments ◽  
Chua's Circuit

In this paper, we discuss a new mechanism for chaos in light of some new developments in the theory of dynamical systems. It was shown in [Wang & Young, 2002b] that strange attractors occur when an autonomous system undergoing a generic Hopf bifurcation is subjected to a weak external forcing that is periodically turned on and off. For illustration purposes, we apply these results to the Chua's system. Derivation of conditions for chaos along with the results of numerical simulations are presented.

STABILITY OF OBSERVER-BASED CHAOTIC COMMUNICATIONS FOR A CLASS OF LUR'E SYSTEMS

2002 ◽  
Vol 12 (07) ◽  
pp. 1605-1618 ◽  
Author(s):  
JOSE ALVAREZ-RAMIREZ ◽  
HECTOR PUEBLA ◽  
ILSE CERVANTES
Keyword(s):  
Numerical Simulations ◽  
Chaotic Oscillator ◽  
Chua’S Circuit ◽  
Lur’E Systems ◽  
Chua's Circuit ◽  
Information Signal ◽  
Synchronization Signal ◽  
Chaotic Communications ◽  
The Stability

In this paper, the stability of observer-based chaotic communications using Lur'e systems is presented. In this approach, the transmitter contains a chaotic oscillator with an input that is modulate by the information signal. The receiver is composed by a copy of the transmitter driven by a synchronization signal. Some effects of transmission noise on the demodulation procedure are discussed. Numerical simulations on Chua's circuit are provided to illustrate our findings.

ANTI-SYNCHRONIZATION OF A CLASS OF COUPLED CHAOTIC SYSTEMS VIA LINEAR FEEDBACK CONTROL

2006 ◽  
Vol 16 (04) ◽  
pp. 1041-1047 ◽  
Author(s):  
CHUANDONG LI ◽  
XIAOFENG LIAO
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Feedback ◽  
Generalized Synchronization ◽  
Lyapunov Stability Theorem ◽  
Linear Feedback Control ◽  
Relevant Variables ◽  
Special Case

As a special case of generalized synchronization, chaos anti-synchronization can be characterized by the vanishing of the sum of relevant variables. In this paper, based on Lyapunov stability theorem for ordinary differential equations, several sufficient conditions for guaranteeing the existence of anti-synchronization in a class of coupled identical chaotic systems via linear feedback or adaptive linear feedback methods are derived. Chua's circuit is presented as an example to demonstrate the effectiveness of the proposed approach by computer simulations.

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