Synchronization via pinning control on general complex networks. (English) Zbl 1266.93071

Yu, Wenwu; Chen, Guanrong; Lü, Jinhu; Kurths, Jürgen

SIAM J. Control Optim. 51, No. 2, 1395-1416 (2013).

Summary: This paper studies synchronization via pinning control on general complex dynamical networks, such as strongly connected networks, networks with a directed spanning tree, weakly connected networks, and directed forests. A criterion for ensuring network synchronization on strongly connected networks is given. It is found that the vertices with very small in-degrees should be pinned first. In addition, it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers, which implies that the vertices with very large out-degrees may be pinned. Then, a criterion for achieving synchronization on networks with a directed spanning tree, which can be composed of many strongly connected components, is derived. It is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls. Moreover, a simple but effective pinning algorithm for reaching synchronization on a general complex dynamical network is proposed. Finally, some simulation examples are given to verify the proposed pinning scheme.

MSC:

93C10	Nonlinear systems in control theory
68M12	Network protocols
93B25	Algebraic methods
93A15	Large-scale systems

Keywords:

complex network; pinning control; synchronization; strongly connected network; directed spanning tree; weakly connected network; directed forest