scholarly journals Weak Projective Synchronization in Drive-Response Dynamical Networks with Time-Varying Delay and Parameter Mismatch

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jiang Xu ◽  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Functional Differential Equations ◽  
Projective Synchronization ◽  
Time Varying ◽  
Error Level ◽  
Parameter Mismatch ◽  
Dynamical Networks ◽  
Time Varying Delay ◽  
Functional Differential ◽  
Varying Delay

This paper investigates the problem of projective synchronization in drive-response dynamical networks (DRDNs) with time-varying delay and parameter mismatch via impulsive control. Owing to projective factor and parameter mismatch, complete projective synchronization cannot be achieved. Therefore, a weak projective synchronization scheme is proposed to ensure that the DRDNs are in a state of synchronization with an error level. Based on the stability analysis of the impulsive functional differential equations, a general method of the weak projective synchronization with the error level is derived in DRDNs. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.

FURTHER RESULTS ON MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY

2008 ◽  
Vol 18 (01) ◽  
pp. 187-202 ◽  
Author(s):  
FERNANDO O. SOUZA ◽  
REINALDO M. PALHARES ◽  
EDUARDO M. A. M. MENDES ◽  
LEONARDO A. B. TÔRRES
Keyword(s):  
Communication Systems ◽  
Functional Differential Equations ◽  
Linear Matrix ◽  
Time Varying ◽  
Lur’E Systems ◽  
New Approach ◽  
Time Varying Delay ◽  
Delay Feedback Control ◽  
Functional Differential ◽  
Varying Delay

In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

scholarly journals Parameters Identification and Synchronization of Chaotic Delayed Systems Containing Uncertainties and Time-Varying Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Zhongkui Sun ◽  
Xiaoli Yang
Keyword(s):  
Dynamical Systems ◽  
Functional Differential Equations ◽  
Parameters Identification ◽  
Time Varying ◽  
Unknown Parameters ◽  
Delayed Systems ◽  
Adaptive Scheme ◽  
Time Varying Delay ◽  
Functional Differential ◽  
Varying Delay

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme.

scholarly journals PINNING IMPULSIVE STABILIZATION OF NONLINEAR DYNAMICAL NETWORKS WITH TIME-VARYING DELAY

2012 ◽  
Vol 22 (07) ◽  
pp. 1250176 ◽  
Author(s):  
JIANQUAN LU ◽  
ZIDONG WANG ◽  
JINDE CAO ◽  
DANIEL W.C. HO ◽  
JÜRGEN KURTHS
Keyword(s):  
Lyapunov Method ◽  
Impulsive Control ◽  
Time Varying ◽  
Impulsive Systems ◽  
Dynamical Networks ◽  
Nonlinear Dynamical ◽  
Time Varying Delay ◽  
Impulsive Control Strategy ◽  
Pinning Impulsive Control ◽  
Varying Delay

In this paper, a new impulsive control strategy, namely pinning impulsive control, is proposed for the stabilization problem of nonlinear dynamical networks with time-varying delay. In this strategy, only a small fraction of nodes is impulsively controlled to globally exponentially stabilize the whole dynamical network. By employing the Lyapunov method combined with the mathematical analysis approach as well as the comparison principle for impulsive systems, some criteria are obtained to guarantee the success of the global exponential stabilization process. The obtained criteria are closely related to the proportion of the controlled nodes, the impulsive strength, the impulsive interval and the time-delay. Numerical examples are given to demonstrate the effectiveness of the designed pinning impulsive controllers.

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