LINEAR GENERALIZED CHAOTIC SYNCHRONIZATION VIA SINGLE CHANNEL

2011 ◽  
Vol 25 (21) ◽  
pp. 2879-2887
Author(s):  
XING-YUAN WANG ◽  
MING-JUN WANG
Keyword(s):  
Numerical Simulations ◽  
Single Channel ◽  
Chaotic Synchronization ◽  
Drive System ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response System ◽  
Replacement Method ◽  
Simulation Results ◽  
Transitional System

In this paper, the drive system and the response system can be in a state of linear generalized synchronization via transmitting single signal. By means of a transitional system, the response system is obtained by variable replacement method. Chen system and hyperchaotic Chen system are used as examples in numerical simulations. Simulation results show the effectiveness of the method.

LINEAR AND NONLINEAR GENERALIZED SYNCHRONIZATION OF CHAOTIC SYSTEMS

2010 ◽  
Vol 24 (31) ◽  
pp. 6143-6155
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
State Observer ◽  
Drive System ◽  
Generalized Synchronization ◽  
Response System ◽  
Linear And Nonlinear ◽  
Synchronization Scheme ◽  
Application Scope

In this paper, the linear and nonlinear generalized synchronization of chaotic systems is investigated. Based on the modified state observer method, a new synchronization approach is proposed with more extensive application scope. The proposed synchronization scheme can realize the linear and nonlinear generalized synchronizations of same dimensional or different dimensional chaotic systems. Sufficient conditions of global asymptotic generalized synchronization between the drive system and the response system are gained on the basis of the state observer theory. Numerical simulations further illustrate the effectiveness of the proposed scheme.

GENERALIZED SYNCHRONIZATION OF CHAOS IN RCL-SHUNTED JOSEPHSON JUNCTIONS BY UNIDIRECTIONALLY COUPLING

2010 ◽  
Vol 24 (29) ◽  
pp. 5675-5682 ◽  
Author(s):  
YU-LING FENG ◽  
XI-HE ZHANG ◽  
ZHI-GANG JIANG ◽  
KE SHEN
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Josephson Junctions ◽  
System Approach ◽  
Chaotic Synchronization ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Maximum Condition ◽  
Two Systems

This paper investigates chaotic synchronization in the generalized sense in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using the means of unidirectionally coupling. The numerical simulations confirm that the generalized synchronization of chaos in these two systems can be achieved with a suitable coupling intensity when the maximum condition Lyapunov exponent (MCLE) is negative. Also, the auxiliary system approach is used to detect the existence of the generalized synchronization.

PROJECTIVE SYNCHRONIZATION OF TWO DIFFERENT DIMENSIONAL NONLINEAR SYSTEMS

2013 ◽  
Vol 27 (21) ◽  
pp. 1350113 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Drive System ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Response System ◽  
Opposite Situation ◽  
The One ◽  
Hyperchaotic Systems

Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the behaviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective.

ROBUST DEAD-BEAT SYNCHRONIZATION AND COMMUNICATION FOR DISCRETE-TIME CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (04) ◽  
pp. 835-846 ◽  
Author(s):  
KUANG-YOW LIAN ◽  
PETER LIU ◽  
CHIAN-SONG CHIU ◽  
TUNG-SHENG CHIANG
Keyword(s):  
Numerical Simulations ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Performance Criterion ◽  
Drive System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chaotic Communication ◽  
Response System

This paper proposes synchronization and chaotic communication for a class of Lur'e type discrete-time chaotic systems. The scalar outputs are suitably chosen in a flexible manner to be linear, nonlinear, or predictive, and along with the drive system are then written in an output injection form. Then with a suitable design of an observer-based response system, dead-beat performance is achieved for synchronization and chaotic communications. Then disturbances in the drive system are considered. Using an ℋ∞performance criterion, the disturbance is attenuated to a prescribed level by solving linear matrix inequalities (LMIs). Numerical simulations are carried out to verify the dead-beat performance.

GENERALIZED SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS BASED ON PARAMETER IDENTIFICATION

2009 ◽  
Vol 23 (22) ◽  
pp. 2593-2606 ◽  
Author(s):  
YONGGUANG YU ◽  
HAN-XIONG LI ◽  
JUNZHI YU
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Generalized Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Response System ◽  
Generalized Lorenz System ◽  
The One

This paper investigates the generalized synchronization issue for two different dimensional chaotic systems with unknown parameters. Based on Lyapunov stability theory and adaptive control theory, an adaptive controller is derived to achieve the generalized synchronization whether the dimension of drive system is greater than the one of the response system or not. Meanwhile, corresponding parameter updating laws can be obtained so as to exactly identify uncertain parameters. This technique has been successfully applied to two examples, the generalized synchronization of hyperchaotic Rössler system and chaotic Lorenz system, chaotic Chen system and generalized Lorenz system. Numerical simulations are finally shown to illustrate the effectiveness of the proposed approach.

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER HYPERCHAOTIC LORENZ SYSTEM

2009 ◽  
Vol 23 (17) ◽  
pp. 2167-2178 ◽  
Author(s):  
TIANSHU WANG ◽  
XINGYUAN WANG
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Lorenz System ◽  
Order System ◽  
Generalized Synchronization ◽  
Response System ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results ◽  
The Stability ◽  
Predictor Corrector

In this paper, a type of new fractional order hyperchaotic Lorenz system is proposed. Based on the fractional calculus predictor-corrector algorithm, the fractional order hyperchaotic Lorenz system is investigated numerically, and the simulation results show that the lowest orders for hyperchaos in hyperchaotic Lorenz system is 3.884. According to the stability theory of fractional order system, an improved state-observer is designed, and the response system of generalized synchronization is obtained analytically, whose feasibility is proved theoretically. The synchronization method is adopted to realize the generalized synchronization of 3.884-order hyperchaotic Lorenz system, and the numerical simulation results verify the effectiveness.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LC OSCILLATOR SYSTEM

2007 ◽  
Vol 21 (20) ◽  
pp. 3643-3655 ◽  
Author(s):  
XINGYUAN WANG ◽  
BIN JIA ◽  
MINGJUN WANG
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Tracking Control ◽  
Drive System ◽  
Oscillator System ◽  
Response System ◽  
Lc Oscillator ◽  
Reference Signals ◽  
The Given

This paper presents an active tracking control strategy of the four-dimensional hyperchaotic LC oscillator system based on the theory of stability of the linear system. This strategy can track all kinds of reference signals. It is also proved that the strategy can make the system converge to any desired smooth orbit exponentially in theory. Numerical simulations have shown that the proposed strategy can not only trace the given reference signals, but the response system can also be in different-structure synchronization with the drive system.

ADAPTIVE GENERALIZED SYNCHRONIZATION OF HYPERCHAOS SYSTEMS

2011 ◽  
Vol 25 (32) ◽  
pp. 4563-4571 ◽  
Author(s):  
XINGYUAN WANG ◽  
YAQIN WANG
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
New Method ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lorenz System ◽  
Linear And Nonlinear ◽  
Simulation Results

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme.

Synchronization of Hyper-Chaotic Lorenz System and its Application in Secure Communication

2011 ◽  
Vol 467-469 ◽  
pp. 437-440 ◽  
Author(s):  
Shao Cheng Qu ◽  
Di Liu ◽  
Li Wang
Keyword(s):  
Lyapunov Stability ◽  
Secure Communication ◽  
Lorenz System ◽  
System Simulation ◽  
Drive System ◽  
Nonlinear Controller ◽  
Response System ◽  
Receiver System ◽  
Useful Signal ◽  
Simulation Results

Synchronization of hyper-chaotic Lorenz system and its application in secure communication is studied. Based on the Lyapunov stability, an active nonlinear controller is presented to achieve synchronization of the drive system and the response system. By the conversion functions, the useful signal is modulated into the drive system, and then a secure communication based on hyper-chaotic masking is derived, which can quickly recover the useful signal from the receiver system. Simulation results illustrate the effectiveness of the proposed method.

Modulation instability in nonlinear chiral fiber

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Demissie Jobir Gelmecha ◽  
Ram Sewak Singh
Keyword(s):  
Theoretical Model ◽  
Numerical Simulations ◽  
Pulse Propagation ◽  
Modulation Instability ◽  
Constitutive Relations ◽  
Gain Spectrum ◽  
Circularly Polarized ◽  
Left Handed ◽  
Simulation Results ◽  
The Difference

AbstractIn this paper, the rigorous derivations of generalized coupled chiral nonlinear Schrödinger equations (CCNLSEs) and their modulation instability analysis have been explored theoretically and computationally. With the consideration of Maxwell’s equations and Post’s constitutive relations, a generalized CCNLSE has been derived, which describes the evolution of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) components propagating through single-core nonlinear chiral fiber. The analysis of modulation instability in nonlinear chiral fiber has been investigated starting from CCNLSEs. Based on a theoretical model and numerical simulations, the difference on the modulation instability gain spectrum in LCP and RCP components through chiral fiber has been analyzed by considering loss and chirality into account. The obtained simulation results have shown that the loss distorts the sidebands of the modulation instability gain spectrum, while chirality modulates the gain for LCP and RCP components in a different manner. This suggests that adjusting chirality strength may control the loss, and nonlinearity simultaneously provides stable modulated pulse propagation.

Sign in / Sign up

Export Citation Format

Share Document