Study on Impulsive Synchronization of Chaotic System by Computing Conditional Lyapunov Exponent

2007 ◽  
Author(s):  
Jiang Fei ◽  
Liu Zhong
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Impulsive Synchronization

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals Experimental study for impulsive synchronization of a discrete chaotic system

2003 ◽  
Vol 52 (7) ◽  
pp. 1589
Author(s):  
Chen Ju-Fang ◽  
Zhang Ru-Yuan ◽  
Peng Jian-Hua
Keyword(s):  
Experimental Study ◽  
Chaotic System ◽  
Impulsive Synchronization

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

A flexible chaotic system with adjustable amplitude, largest Lyapunov exponent, and local Kaplan–Yorke dimension and its usage in engineering applications

2018 ◽  
Vol 92 (4) ◽  
pp. 1791-1800 ◽  
Author(s):  
Heng Chen ◽  
Atiyeh Bayani ◽  
Akif Akgul ◽  
Mohammad-Ali Jafari ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Largest Lyapunov Exponent ◽  
Engineering Applications

scholarly journals SUPREME LOCAL LYAPUNOV EXPONENTS AND CHAOTIC IMPULSIVE SYNCHRONIZATION

2013 ◽  
Vol 23 (10) ◽  
pp. 1350169 ◽  
Author(s):  
SHENGYAO CHEN ◽  
FENG XI ◽  
ZHONG LIU
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Local Instability ◽  
Impulsive Synchronization ◽  
Local Lyapunov Exponent ◽  
Expansion Behavior

Impulsively synchronized chaos with criterion from conditional Lyapunov exponent is often interrupted by desynchronized bursts. This is because the Lyapunov exponent cannot characterize local instability of synchronized attractor. To predict the possibility of the local instability, we introduce a concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum of local Lyapunov exponents over the attractor. The SLLE is independent of the system trajectories and therefore, can characterize the extreme expansion behavior in all local regions with prescribed finite-time interval. It is shown that the impulsively synchronized chaos can be kept forever if the largest SLLE of error dynamical systems is negative and then the burst behavior will not appear. In addition, the impulsive synchronization with negative SLLE allows large synchronizable impulsive interval, which is significant for applications.

Impulsive Synchronization of Lü Chaotic System Based on Small Impulsive Signal

2007 ◽  
Vol 47 (3) ◽  
pp. 797-804 ◽  
Author(s):  
Zhijun Peng ◽  
Yang Li ◽  
Xiaofeng Liao ◽  
Chuandong Li
Keyword(s):  
Chaotic System ◽  
Impulsive Synchronization

Circuit Design Contains a Class of Squared Term Lorenz Family Chaotic System

2014 ◽  
Vol 602-605 ◽  
pp. 2684-2687
Author(s):  
Yu Zhang ◽  
Chong Lou Tong ◽  
Teng Fei Lei
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Circuit Design ◽  
Chaotic System ◽  
Lorenz System ◽  
Three Dimensional ◽  
System Stability ◽  
Experimental Simulation ◽  
Chaotic Circuit ◽  
New Class

A new class of three-dimensional chaotic system is constructed by algebraic methods, which has a similar structure with the classic Lorenz system but contains the square term. The equilibrium point of the system stability is analyzed, and the numerical simulation is carried on the bifurcation diagram and Lyapunov exponent. The chaotic circuit of these systems is designed by using the software of EWB. The results of the experimental simulation verify the existence of the chaotic attractor, which provides theoretical reference to the application of such system.

Sign in / Sign up

Export Citation Format

Share Document