Synchronization Of Fractional-order Dynamical Networks Via Intermittent Control

As a new branch of complexity science,complex networks exist widely in the daily life,such as the Internet,epidemic spreading networks,biological networks,economic networks,and so on.In the past decade years,the study of complex networks has attracted widespread interest by researchers in many areas including physics,mathematics,biology,engineering and so on.In particular,there has been extensively investigated in the study of synchronization of complex networks.Synchronization is not only a typical collective behavior,but also a important dynamics character in complex networks.It has been found in different forms both in nature and man-made systems,such as physics,chemistry,biology,engineering,economy and social sciences.This paper mainly studies the synchronization of fractional-order networks via intermittent control.Firstly,the cluster synchronization of fractional-order network has been investigated via in-termittent pinning control.It was supposed that the dynamical behaviors of nodes belonging to the same clusters are identical,but the nodes in different clusters are nonidentical.Combined with proper intermittent controllers,the network achieves cluster synchronization with an irre-ducible coupling matrix,and we obtain a synchronization criterion through the stability theory of fractional-order differential equations and mathematical analysis technique.Specifically,our proposed method is applicable to general networks,where the coupling topology between nodes is directed and weighted,which means the outer coupling matrix is assumed to be asymmetric and not all elements on the non-diagonal are equal to one.Remarkably,an effective way to achieve cluster synchronization is introduced through enhancing some coupling weights.The effectiveness of the obtained theoretical results are verified by numerical simulations.Secondly,the synchronization of fractional-order complex networks under aperiodically in-termittent pinning control is investigated.We mainly focus on the problem how to achieve the synchronization of a complex fractional-order network,then the aperiodically intermittent pinning control is adopted and effective controllers for synchronization are designed.Finally,numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization criteri-a.Thirdly,we extend the above results to the complex-variable network.This is to say,we inves-tigate the synchronization of fractional-order complex-variable complex networks via aperiodically intermittent pinning control.Based on the Lyapunov function method and mathematical analysis theory,we give some synchronization criteria.In the end,we give two numerical simulations to verify the derived theoretical results.Finally;we summarize the main ideas of this paper,discuss some results about intermittent control;and put forward some issues deserving further studies.