Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection

2014 ◽  
Vol 25 (05) ◽  
pp. 1440011 ◽  
Author(s):  
Xiangyong Chen ◽  
Chengyong Wang ◽  
Jianlong Qiu
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Symmetric Structure ◽  
Direct Design

This paper considers the synchronization and anti-synchronization problem of N different coupled chaotic systems with ring connections. Employing the direct design method to design the synchronization and anti-synchronization controllers which can transform the error systems into a stable system with special anti-symmetric structure. Some simple stability criteria are then derived for reaching the synchronization in such systems. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical.

scholarly journals Synchronization of Coupled Chaotic Systems with Ring Connection Based on Special Antisymmetric Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiangyong Chen ◽  
Jianlong Qiu ◽  
Qiang Song ◽  
Ancai Zhang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Complete Synchronization ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System

This paper considers the complete synchronization problem for coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Cuimei Jiang ◽  
Akbar Zada ◽  
M. Tamer Şenel ◽  
Tongxing Li
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Order Error ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System ◽  
Theoretical Results

Abstract This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

scholarly journals Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ling Guo ◽  
Xiaohong Nian ◽  
Huan Pan
Keyword(s):  
Chaotic Systems ◽  
Matrix Theory ◽  
Design Method ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Synchronization Problem ◽  
Direct Design ◽  
The Stability ◽  
Different Chaotic Systems

The generalized synchronization problem is studied in this paper for different chaotic systems with the aid of the direct design method. Based on Lyapunov stability theory and matrix theory, some sufficient conditions guaranteeing the stability of a nonlinear system with nonnegative off-diagonal structure are obtained. Then the control scheme is designed from the stable system by the direct design method. Finally, two numerical simulations are provided to verify the effectiveness and feasibility of the proposed method.

scholarly journals Synchronization and Antisynchronization of N-Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Cuimei Jiang ◽  
Shutang Liu
Keyword(s):  
Permanent Magnet ◽  
Chaotic Systems ◽  
Design Method ◽  
Permanent Magnet Synchronous Motor ◽  
Mathematical Expression ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Direct Design ◽  
General Complex ◽  
Complex Chaotic Systems

This paper discusses synchronization and antisynchronization of N-coupled complex permanent magnet synchronous motors systems with ring connection. Based on the direct design method and antisymmetric structure, the appropriate controllers are designed to ensure the occurrence of synchronization and antisynchronization in an array of N-coupled general complex chaotic systems described by a unified mathematical expression with ring connection. The proposed method is flexible and is suitable both for design and for implementation in practice. Numerical results are plotted to show the rapid convergence of errors to zero and further verify the effectiveness and feasibility of the theoretical scheme.

Hybrid Synchronization of Three Identical Coupled Chaotic Systems Using the Direct Design Method

2014 ◽  
Vol 912-914 ◽  
pp. 695-699 ◽  
Author(s):  
Xiu Huan Ji
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Stability Criterion ◽  
Chaotic Systems ◽  
Design Method ◽  
Complete Synchronization ◽  
Numerical Example ◽  
Direct Design ◽  
Error System ◽  
Hybrid Synchronization

This paper investigates the hybrid synchronization behavior (coexistence of anti-synchronization and complete synchronization) in three coupled chaotic systems with ring connections. We employ the direct design method to design the hybird synchronization controllers, which transform the error system into a nonlinear system with a special antisymmetric structure. A simple stability criterion is then derived for reaching hybrid synchronization. Finally, numerical example is provided to demonstrate the effectiveness of the theoretical analysis.

Adaptive Modified Projective Synchronization Between Genesio and Rossler Chaotic Systems with Uncertainties

2012 ◽  
Vol 546-547 ◽  
pp. 1040-1044 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Ji Fei Liu ◽  
Rui Pan
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Projective Synchronization ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Control Laws ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Modified Projective Synchronization ◽  
Different Chaotic Systems

The paper discusses the modified projective synchronization of two different chaotic systems by nonlinear control laws, considering the conditions of the master-slave systems with uncertain parameters, the synchronization problem between Genesio system and Rossler system has been investigated, adopting the adaptive control method, a sufficient condition is attainted for the modified projective synchronization between master and slave system, finally, The control performances are verified by the numerical examples.

ANALYSIS AND SYNTHESIS OF RADIATION PATTERNS FROM CIRCULAR APERTURES

1960 ◽  
Vol 38 (1) ◽  
pp. 78-99 ◽  
Author(s):  
A. Ishimaru ◽  
G. Held
Keyword(s):  
Radiation Pattern ◽  
Traveling Wave ◽  
Design Method ◽  
Source Distribution ◽  
Circular Aperture ◽  
Narrow Beam ◽  
Wave Type ◽  
Numerical Examples ◽  
Analysis And Synthesis ◽  
Improved Design

Part I considers the problem of determining the source distribution over a circular aperture required to produce a prescribed radiation pattern. In particular, the problem of optimizing the narrow broadside pattern from a circular aperture is discussed in detail and an improved design method over Taylor's for line source is devised. Numerical examples are given.Part II deals with the analysis of the radiation pattern from a circular aperture from γ1 to γ2 with the traveling wave type source functions. Expressions suitable to the analysis and the synthesis are obtained and the narrow-beam and shaped-beam synthesis are discussed.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

scholarly journals A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm

2015 ◽  
Vol 5 (1) ◽  
pp. 739-747 ◽  
Author(s):  
I. Ahmad ◽  
A. Saaban ◽  
A. Ibrahin ◽  
M. Shahzad
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Control Techniques ◽  
Synchronization Problem ◽  
Response Systems ◽  
Globally Stable ◽  
Time Evaluation

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9.

scholarly journals Symmetric Oscillator: Special Features, Realization, and Combination Synchronization

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2142
Author(s):  
Victor Kamdoum Tamba ◽  
Janarthanan Ramadoss ◽  
Viet-Thanh Pham ◽  
Giuseppe Grassi ◽  
Othman Abdullah Almatroud ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Numerical Examples ◽  
Combination Synchronization ◽  
Significant Attention

Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscillator’s dynamics. Moreover, the combined synchronization of two drives and one response oscillator is reported. Numerical examples illustrate the correction of our approach.

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