scholarly journals Combination Difference Synchronization between Identical Generalised Lotka-Volterra Chaotic Systems

2020 ◽  
Vol 12 (2) ◽  
pp. 183-188 ◽  
Author(s):  
P. Trikha ◽  
Nasreen ◽  
L. S. Jahanzaib
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Complete Agreement ◽  
Theoretical Results ◽  
Combination Difference

This manuscript investigates the combination difference synchronization between identical Generalised Lotka-Volterra Chaotic Systems. Numerical Simulations have been performed which are in complete agreement of theoretical results.

scholarly journals Compound Difference Anti-Synchronization between Hyper-Chaotic Systems of Fractional Order

2020 ◽  
Vol 12 (2) ◽  
pp. 175-181 ◽  
Author(s):  
A. Khan ◽  
L. S. Jahanzaib ◽  
Nasreen ◽  
P. Trikha ◽  
T. Khan
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Theoretical Results

In this article, the compound difference anti-synchronization between fractional order hyper-chaotic systems have been studied. Numerical simulations have been performed using MATLAB to verify the theoretical results on fractional order Xling, Vanderpol, Rikitake and Rabinovich hyper-chaotic systems.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

ANALYTICAL CONDITIONS FOR AMPLITUDE DEATH INDUCED BY CONJUGATE VARIABLE COUPLINGS

2011 ◽  
Vol 21 (01) ◽  
pp. 225-235 ◽  
Author(s):  
XIAOMING ZHANG ◽  
YINGCHUN WU ◽  
JIANHUA PENG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Arbitrary Number ◽  
Chaotic Systems ◽  
Amplitude Death ◽  
Chaotic Oscillators ◽  
Conjugate Variable ◽  
Global Coupling ◽  
Theoretical Results

We construct local and global conjugate variable coupled chaotic systems with an arbitrary number of identical chaotic oscillators. Amplitude death phenomena are found in these two kinds of systems. General methods are proposed to theoretically analyze conditions for amplitude death under local and global conditions, respectively. Taking the Rössler chaotic system as the oscillator unit, we apply these methods to determine the analytical conditions for amplitude death. And the transition relations between local and global coupling induced amplitude deaths are also given. All theoretical results are well confirmed by numerical simulations.

scholarly journals Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

2021 ◽  
Vol 26 (6) ◽  
pp. 993-1011
Author(s):  
Mei Liu ◽  
Jie Chen ◽  
Haijun Jiang ◽  
Zhiyong Yu ◽  
Cheng Hu ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Adaptive Strategy ◽  
Auxiliary Function ◽  
Intermittent Control ◽  
Global Synchronization ◽  
Delayed Systems ◽  
Control Gain ◽  
Analysis Technique ◽  
Theoretical Results

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.

Active Control for Multi-Switching Combination Synchronization of Non-Identical Chaotic Systems

2018 ◽  
pp. 129-162 ◽  
Author(s):  
Shikha Singh ◽  
Ahmad Taher Azar ◽  
Muzaffar Ahmad Bhat ◽  
Sundarapandian Vaidyanathan ◽  
Adel Ouannas
Keyword(s):  
Information Security ◽  
Numerical Simulations ◽  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Slave System ◽  
Combination Synchronization ◽  
Wide Range ◽  
Synchronization Scheme ◽  
Theoretical Results

This chapter investigates the multi-switching combination synchronization of three non-identical chaotic systems via active control technique. In recent years, some advances have been made with the idea of multi-switching combination synchronization. The different states of the master systems are synchronized with the desired state of the slave system in multi-switching combination synchronization scheme. The relevance of such kinds of synchronization studies to information security is evident in the wide range of possible synchronization directions that exist due to multi-switching synchronization. Numerical simulations justify the validity of the theoretical results discussed.

scholarly journals Simultaneity of Synchronization and Antisynchronization in a Class of Chaotic Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhi Liu ◽  
Rongwei Guo ◽  
Yi Qi ◽  
Cuimei Jiang
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Synchronization Phenomenon ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Theoretical Results

In this paper, a new synchronization phenomenon, that is, the simultaneity of synchronization and antisynchronization, is investigated for a class of chaotic systems. First, for a given chaotic system, necessary and sufficient conditions for the simultaneity of synchronization and antisynchronization are proved. Then, based on these conditions, all solutions of such synchronization phenomenon for a given chaotic system are derived. After that, physical controllers that are not only simple but also implementable are designed to realize the simultaneity of synchronization and antisynchronization in the above system. Finally, illustrative examples based on numerical simulations are used to verify the validity and effectiveness of the above theoretical results.

STUDY OF GLOBALLY EXPONENTIAL SYNCHRONIZATION FOR THE FAMILY OF RÖSSLER SYSTEMS

2006 ◽  
Vol 16 (08) ◽  
pp. 2395-2406 ◽  
Author(s):  
XIAOXIN LIAO ◽  
PEI YU
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Functions ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Exponential Synchronization ◽  
Nonlinear Feedback ◽  
Feedback Controls ◽  
The Family ◽  
Control And Synchronization ◽  
Theoretical Results

This paper considers the globally exponential synchronization (GES) of the family of Rössler chaotic systems. One pair of the six transmitter-receiver systems is specifically studied, and algebraic criterion for the GES is obtained via proper nonlinear feedback controls. Based on the study of the systems' structures, appropriate Lyapunov functions are constructed for error systems. The method presented in this paper provides a convenient tool in the practical use of chaos control and synchronization. Numerical simulations are provided to demonstrate the theoretical results.

scholarly journals Impulsive Control of Memristive Chaotic Systems with Impulsive Time Window

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
FuLi Chen ◽  
Hui Wang ◽  
Chuandong Li
Keyword(s):  
Numerical Simulations ◽  
Comparison Principle ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Time Window ◽  
Time Windows ◽  
Chaotic Circuit ◽  
Asymptotic Stabilization ◽  
Theoretical Results

The problem of impulsive control for memristor-based chaotic circuit systems with impulsive time windows is investigated. Based on comparison principle, several novel criteria which guarantee the asymptotic stabilization of the memristor-based chaotic circuit systems are obtained. In comparison with previous results, the present results are easily verified. Numerical simulations are given to further illustrate the effectiveness of the theoretical results.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

Sign in / Sign up

Export Citation Format

Share Document