國立清華大學 數學系

Abstract In this talk, we introduce an iterative approach to global cluster synchronization of complex networks with a community structure. The units comprising the network are described by differential equations, and units in the different communities can be governed by different equations. The coupling configuration of the network is rather general with coupling terms that could be nonlinear and with heterogeneous coupling time delays. The connection matrix could be time-dependent and could contain mixed signs of off-diagonal entries. Based on this approach, both delay-dependent and delay-independent criteria for global cluster synchronization are derived. We implement the present approach for a nonlinearly coupled neural network with heterogeneous coupling delays. Several numerical examples are given to show that neural networks can exhibit new and rich collective behavior, which is distinct from the individual behavior of isolated neurons, under the synchronization criteria.