Partial component synchronization on chaotic networks.

Abstract As for the dynamical networks which consist of some high-dimensional nonlinear systems, the problems that researchers are concerned with are usually the asymptotic convergence on some components (rather than all components) of node's state variables under certain condition. This means that partial component synchronization is more meaningful than identical synchronization in some cases. In this paper, the definition of partial component synchronization is given, and then the problem of partial component synchronization on a class of chaotic dynamical networks is investigated. By using matrix theory, stability theory and the hypothesis that several components in the solution vector of a single uncoupled node are ultimately dissipative, some sufficient conditions on partial component synchronization in the chaotic dynamical networks are derived. Finally, numerical simulations are shown to demonstrate the correctness of the theoretical results. Highlights • Partial component synchronization is a kind of group dynamics behavior weaker than identical synchronization. • In this paper, the definition of partial component synchronization is given, and the stability theory of partial variables is applied to study it. • Several sufficient conditions for partial component synchronization to be realized on the network are derived. [ABSTRACT FROM AUTHOR]