scholarly journals Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Wang ◽  
Kejun Wang ◽  
Nuo Jia
Keyword(s):  
Chaotic System ◽  
Chaos Control ◽  
Control Strategies ◽  
Direct Method ◽  
Projective Synchronization ◽  
Complete Synchronization ◽  
Unknown Parameters ◽  
Feedback Controllers ◽  
Adaptive Parameter ◽  
Hybrid Projective Synchronization

Adaptive feedback controllers based on Lyapunov's direct method for chaos control and hybrid projective synchronization (HPS) of a novel 3D chaotic system are proposed. Especially, the controller can be simplified ulteriorly into a single scalar one to achieve complete synchronization. The HPS between two nearly identical chaotic systems with unknown parameters is also studied, and adaptive parameter update laws are developed. Numerical simulations are demonstrated to verify the effectiveness of the control strategies.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE UNIFIED CHAOTIC SYSTEM

2009 ◽  
Vol 23 (15) ◽  
pp. 1913-1921 ◽  
Author(s):  
XINGYUAN WANG ◽  
JUNMEI SONG
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Response System ◽  
Unified Chaotic System ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper studies the adaptive full state hybrid projective synchronization method. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with known or unknown parameters asymptotically full state hybrid projective synchronized. A unified chaotic system is used as an example and numerical simulations show the effectiveness of the scheme.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION OF UNIFIED CHAOTIC SYSTEM WITH UNKNOWN PARAMETERS

2011 ◽  
Vol 25 (32) ◽  
pp. 4661-4666 ◽  
Author(s):  
XING-YUAN WANG ◽  
LE-BIAO ZHU
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Response System ◽  
Unified Chaotic System ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme.

scholarly journals Parameter Estimation of a Class One-Dimensional Discrete Chaotic System

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Lidong Liu ◽  
Jinfeng Hu ◽  
Huiyong Li ◽  
Jun Li ◽  
Zishu He ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Chaotic System ◽  
Chaos Control ◽  
Mean Value ◽  
Unknown Parameters ◽  
Tent Map ◽  
One Dimensional ◽  
Chebyshev Map ◽  
Mean Value Method ◽  
Control And Synchronization

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method (MVM). It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exact than MVM. Finally, numerical simulations on Chebyshev map and Tent map show that the proposed method has better performance of parameter estimation than MVM.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

2008 ◽  
Vol 22 (24) ◽  
pp. 4175-4188 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Communication Scheme ◽  
Simulation Results ◽  
Feedback Method

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

scholarly journals Chaos synchronization in fractional differential systems

2013 ◽  
Vol 371 (1990) ◽  
pp. 20120155 ◽  
Author(s):  
Fengrong Zhang ◽  
Guanrong Chen ◽  
Changpin Li ◽  
Jürgen Kurths
Keyword(s):  
Chaos Synchronization ◽  
Projective Synchronization ◽  
Generalized Synchronization ◽  
Complete Synchronization ◽  
Differential Systems ◽  
Function Projective Synchronization ◽  
Fractional Differential Systems ◽  
Recent Developments ◽  
Fractional Differential ◽  
Hybrid Projective Synchronization

This paper presents a brief overview of recent developments in chaos synchronization in coupled fractional differential systems, where the original viewpoints are retained. In addition to complete synchronization, several other extended concepts of synchronization, such as projective synchronization, hybrid projective synchronization, function projective synchronization, generalized synchronization and generalized projective synchronization in fractional differential systems, are reviewed.

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