Synchronization of the Time-Varying Discrete Biological Networks

The study of synchronization 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 is timely evolving and spatially extended. Thus the time-invariant discrete biological networks are often insufficient to capture the key features of real-world biological networks. Here, a time-varying discrete biological network is proposed to characterize the practical metapopulation for the first time. Based on this model, several novel local synchronous criteria are then attained, which provide some new insights into the ecological conservation and biological diversity. Moreover, these synchronous criteria are also applicable to the synchronization of complex networks in other biological and engineering systems.