Partial synchronization in linearly and symmetrically coupled ordinary differential systems

In this paper, we discuss partial synchronization of linearly and symmetrically coupled ordinary differential equations (LSCODEs). The synchronization phenomena are investigated via invariant synchronization manifolds. On the basis of geometrical analysis of the synchronization manifold, several criteria for the global attractivity of the invariant synchronization manifold are obtained. Combining these criteria with some numerical examples, we investigate how topological structure affects partial synchronization, and give a valuable discussion about the possibility of partial synchronization with increasing coupling strength.