Synchronization for discrete-time complex networks with probabilistic time delays

2019 ◽  
Vol 525 ◽  
pp. 1088-1101 ◽  
Author(s):  
Ranran Cheng ◽  
Mingshu Peng ◽  
Jinchen Yu ◽  
Haifen Li
Keyword(s):  
Complex Networks ◽  
Discrete Time ◽  
Time Delays

scholarly journals Global Synchronization of Complex Networks with Discrete Time Delays on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Quanxin Cheng ◽  
Jinde Cao
Keyword(s):  
Complex Networks ◽  
Time Scales ◽  
Discrete Time ◽  
Time Delays ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Global Synchronization ◽  
Synchronization Problem

This paper studies the global synchronization problem for a class of complex networks with discrete time delays. By using the theory of calculus on time scales, the properties of Kronecker product, and Lyapunov method, some sufficient conditions are obtained to ensure the global synchronization of the complex networks with delays on time scales. These sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). The main contribution of the result is that the global synchronization problems with both discrete time and continuous time are unified under the same framework.

ON SYNCHRONIZATION OF DISCRETE-TIME MARKOVIAN JUMPING STOCHASTIC COMPLEX NETWORKS WITH MODE-DEPENDENT MIXED TIME-DELAYS

2009 ◽  
Vol 23 (03) ◽  
pp. 411-434 ◽  
Author(s):  
YURONG LIU ◽  
ZIDONG WANG ◽  
XIAOHUI LIU
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Discrete Time ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Disturbances ◽  
Coupling Term ◽  
Markovian Jumping

In this paper, the synchronization problem is investigated for a new class of discrete-time complex networks. Such complex networks involve the Markovian jumping parameters, mode-dependent discrete and distributed time-delays, constant and delayed couplings, as well as multiple stochastic disturbances. The stochastic disturbances influence the constant coupling term, the delayed coupling term, as well as the overall network dynamics, which could better describe the dynamical behavior of a coupled complex network presented within a noisy environment. With help from the Lyapunov functional method and the properties of Kronecker product, we employ the stochastic analysis techniques to derive several delay-dependent sufficient conditions under which the coupled complex network is asymptotically synchronized in the mean square. The criteria obtained in this paper are in the form of LMIs whose solution can be easily calculated using the standard numerical software. It is shown that our main results can cover many existing ones reported in the literature. A numerical example is presented to illustrate the usefulness of our results.

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