Synchronization of fractional-order spatiotemporal complex networks with boundary communication

This article is dedicated to the synchronization problem of fractional-order spatiotemporal networks with boundary coupling. Above all, instead of the traditional coupling form at the whole space, a type of boundary communication mechanism is proposed for fractional-order spatiotemporal networks, where nodes interact each other only at the spatial boundary. Subsequently, based on fractional-order inequalities and various analytical skills, some synchronization criteria are derived for the addressed networks with boundary constant weights or time-varying weights. Particularly, an adaptive scheme and its pinning form are designed to update time-varying coupling weights only based on the states information at the boundary position, which are more effective and convenient compared to the existing adaptive strategies dependent of states information in whole space. In addition, a rigorous theoretical analysis is developed for fractional-order adaptive strategy, which provides a new analytic method for adaptive control of fractional-order models. Lastly, the theoretical analysis is confirmed by a numerical example