Partial synchronization in community networks based on the intra- community connections

Abstract

In this paper, we propose a novel criterion on the partial synchronization in a generalized linearly coupled network by employing Lyapunov stability theory and linear matrix inequality. The obtained criterion is only dependent on intra-community connections, and the information of inter-community connections is not necessary. Therefore, it provides more convenience in reducing network sizes in practice. Compared with the previous classical criterion, the threshold derived from the obtained criterion is no less than the classical threshold. We give some particular cases in which the obtained threshold is equal to the classical threshold. Finally, we show numerical simulations to verify the validity of the proposed criteria and comparisons.

Keywords

• community network
• partial synchronization
• invariant manifold
• intra-community connection