On pinning synchronization of complex dynamical networks

The study of coherence of population dynamics is extremely important for predicting and evaluating the risk of global extinctions. The migration in a network of patch populations (metapopulation) inevitably involves various environmental noises or outside disturbances, which make the migration model time evolving and spatially extended. Thus time-invariant discrete ecological networks are often insufficient to capture the key features of real-world dynamical networks. Here, a time-varying discrete ecological network is proposed to characterize the practical metapopulation for the first time. Based on this model, several novel local coherence criteria are then attained, which provide some new insights into ecological conservation and biological diversity. Moreover, these coherence criteria are also applicable to the synchronization of complex networks in other biological and engineering systems.