SYNCHRONIZATION CRITERIA FOR COUPLED CHAOTIC SYSTEMS WITH PARAMETER MISMATCHES

2011 ◽  
Vol 25 (18) ◽  
pp. 2493-2506 ◽  
Author(s):  
MIHUA MA ◽  
JIANPING CAI
Keyword(s):  
Error Bound ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Synchronization Error ◽  
Slave System ◽  
Numerical Examples ◽  
Error Variable

This paper studies synchronization between two linearly coupled non-autonomous chaotic systems with parameter mismatches. Based on Lyapunov's stability theory and Sylvester's criterion, some algebraic criteria are derived to synchronize the master and slave system with error bound. Besides, the largest synchronization error can be estimated analytically. Some numerical examples are presented to verify the effectiveness of these criteria. In the examples, the estimated largest synchronization error is compared with the evolution of the error variable, which further shows that the present techniques are effective.

scholarly journals Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chenhui Wang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Numerical Examples ◽  
Mode Synchronization ◽  
Fractional Order Integral

Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods.

scholarly journals SYNCHRONIZATION OF A CLASS OF MASTER–SLAVE NONAUTONOMOUS CHAOTIC SYSTEMS WITH PARAMETER MISMATCH VIA SINUSOIDAL FEEDBACK CONTROL

2011 ◽  
Vol 25 (16) ◽  
pp. 2195-2215 ◽  
Author(s):  
JIANPING CAI ◽  
MIHUA MA ◽  
XIAOFENG WU
Keyword(s):  
Feedback Control ◽  
Error Bound ◽  
Error Bounds ◽  
Chaotic Systems ◽  
Direct Method ◽  
Harmonic Excitation ◽  
Synchronization Error ◽  
Error Feedback ◽  
Parameter Mismatch ◽  
State Error

In this paper, we investigate a master–slave synchronization scheme of two n-dimensional nonautonomous chaotic systems coupled by sinusoidal state error feedback control, where parameter mismatch exists between the external harmonic excitation of master system and that of slave one. A concept of synchronization with error bound is introduced due to parameter mismatch, and then the bounds of synchronization error are estimated analytically. Some synchronization criteria are firstly obtained in the form of matrix inequalities by the Lyapunov direct method, and then simplified into some algebraic inequalities by the Gerschgorin disc theorem. The relationship between the estimated synchronization error bound and system parameters reveals that the synchronization error can be controlled as small as possible by increasing the coupling strength or decreasing the magnitude of mismatch. A three-dimensional gyrostat system is chosen as an example to verify the effectiveness of these criteria, and the estimated synchronization error bounds are compared with the numerical error bounds. Both the theoretical and numerical results show that the present sinusoidal state error feedback control is effective for the synchronization. Numerical examples verify that the present control is robust against amplitude or phase mismatch.

scholarly journals Bipartite Synchronization of Heterogeneous Signed Networks with Distributed Impulsive Control

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Guizhen Feng ◽  
Jian Ding ◽  
Jinde Cao ◽  
Qingqing Cao
Keyword(s):  
Error Bound ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Mathematical Expression ◽  
Synchronization Error ◽  
Error Level ◽  
Numerical Examples ◽  
Signed Networks ◽  
Average Impulsive Interval ◽  
Theoretical Results

This study investigates the bipartite synchronization of heterogeneous signed networks with distributed impulsive control. Leader-follower bipartite synchronization within a nonzero error bound is analyzed when the average impulsive interval is T a < ∞ or T a = ∞ . Some sufficient conditions to achieve the bipartite quasi-synchronization are presented, and the synchronization error level is estimated by the specific mathematical expression. The correctness of the theoretical results is verified by numerical examples.

scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

scholarly journals Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Marcio Eisencraft ◽  
Renato D. Fanganiello ◽  
Luiz A. Baccala
Keyword(s):  
Discrete Time ◽  
Digital Filter ◽  
Feedback Loop ◽  
Chaotic Systems ◽  
Signal Propagation ◽  
Slave System ◽  
Spectral Content ◽  
Channel Bandwidth ◽  
System Synchronization ◽  
Transmitted Signal

Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

scholarly journals Study on Chaotic Fault Tolerant Synchronization Control Based on Adaptive Observer

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dongming Chen ◽  
Xinyu Huang ◽  
Tao Ren
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Adaptive Observer ◽  
Synchronization Control ◽  
Slave System ◽  
Chen System ◽  
Master System ◽  
Abrupt Faults

Aiming at the abrupt faults of the chaotic system, an adaptive observer is proposed to trace the states of the master system. The sufficient conditions for synchronization of such chaotic systems are also derived. Then the feasibility and effectiveness of the proposed method are illustrated via numerical simulations of chaotic Chen system. Finally, the proposed synchronization schemes are applied to secure communication system successfully. The experimental results demonstrate that the employed observer can manage real-time fault diagnosis and parameter identification as well as states tracing of the master system, and so the synchronization of master system and slave system is achieved.

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.

scholarly journals New error bound for linear complementarity problem of $ S $-$ SDDS $-$ B $ matrices

2022 ◽  
Vol 7 (2) ◽  
pp. 3239-3249
Author(s):  
Lanlan Liu ◽  
◽  
Pan Han ◽  
Feng Wang
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Numerical Examples

<abstract><p>$ S $-$ SDDS $-$ B $ matrices is a subclass of $ P $-matrices which contains $ B $-matrices. New error bound of the linear complementarity problem for $ S $-$ SDDS $-$ B $ matrices is presented, which improves the corresponding result in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Numerical examples are given to verify the corresponding results.</p></abstract>

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Error Bound ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Time Stepping ◽  
Theoretical Results

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

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