Design of Dynamic Controller for the Synchronization of Complex Dynamical Networks with a Coupling Delay

2019 ◽  
pp. 211-235
Author(s):  
Ju H. Park ◽  
Tae H. Lee ◽  
Yajuan Liu ◽  
Jun Chen
Keyword(s):  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Coupling Delay ◽  
Dynamic Controller

scholarly journals Sampled-Data Synchronization for Complex Dynamical Networks with Time-Varying Coupling Delay and Random Coupling Strengths

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Jian-An Wang ◽  
Xin-Yu Wen
Keyword(s):  
Sampling Period ◽  
Complex Dynamical Networks ◽  
Data Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Sampled Data ◽  
Dynamical Networks ◽  
Coupling Delay ◽  
Coupling Strengths ◽  
Random Coupling

This paper is concerned with the problem of sampled-data synchronization for complex dynamical networks (CDNs) with time-varying coupling delay and random coupling strengths. The random coupling strengths are described by normal distribution. The sampling period considered here is assumed to be less than a given bound. By taking the characteristic of sampled-data system into account, a discontinuous Lyapunov functional is constructed, and a delay-dependent mean square synchronization criterion is derived. Based on the proposed condition, a set of desired sampled-data controllers are designed in terms of linear matrix inequalities (LMIs) that can be solved effectively by using MATLAB LMI Toolbox. Numerical examples are given to demonstrate the effectiveness of the proposed scheme.

Bifurcation Analysis of Synchronized Regions in Complex Dynamical Networks with Coupling Delay

2014 ◽  
Vol 24 (01) ◽  
pp. 1450011 ◽  
Author(s):  
Longkun Tang ◽  
Jun-An Lu ◽  
Jinhu Lü ◽  
Xiaoqun Wu
Keyword(s):  
Time Delay ◽  
Bifurcation Analysis ◽  
Complex Dynamical Networks ◽  
Stability Function ◽  
Dynamical Networks ◽  
Synchronous State ◽  
Coupling Delay ◽  
Numerical Investigations ◽  
Small Delay ◽  
Synchronized Region

According to the master stability function (MSF) framework, synchronized regions play an extremely important role in network synchronization. On these grounds, this paper casts sight on network synchronous state stability via studying the bifurcation (or transition) problem of network synchronized regions with varying nodal dynamics, and the effects of time delay on the bifurcation of synchronized regions. Theoretical and numerical investigations show that in complex networks with coupling delay, there exist rich bifurcation behaviors of synchronized regions. The coupling delay can not only enlarge or narrow synchronized regions, but also change bifurcation points. More importantly, a very small delay can result in the conversion of an unbounded or empty synchronized region into a bounded one, implying that coupling delay can enhance or suppress synchronization in complex dynamical networks. These results will further strengthen our understanding for synchronous state stability in complex dynamical networks.

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