Synchronization Of Delayed Complex Dynamical Networks Based On Switching Topology

Complex dynamical networks have been extensively studied inmany fields, from physics and mathematics to neurobiology and socialsciences. Synchronization, as one of the most important problems ofcomplex dynamical networks, has attracted increasing interest. It is alsoa common phenomenon which can be witnessed in many practicalsystems such as power grids, information processing, communication.However, the connection topology of a network may change due to linkfailure or creation of new nodes in a network which makes the analysis ofthe behavior of the network more complex. Taking a power grid as anexample, it is well known that the power system can work properly onlyif the generators are kept in synchronism. Loss of synchronization may becaused by a severe fault in a local power system. Synchronization of thepower grid can be recovered by adjusting connection topology ofgenerators. Besides, the nodes themselves and the coupling betweendifferent nodes may have delays. Thus, it is of great theoretical andpractical significance to study the synchronization of delayed complexdynamical networks based on switching topology. The main content ofthis paper is as following:1Synchronization of continuous switched network with delay innodes themselves is studied. The single Lyapunov and multiply Lyapunovfunction methods are used to obtain the synchronization criteria andcorresponding switching laws for nodes with both discrete and distributeddelay.2Synchronization of continuous switched network with couplingdelay is investigated. The discrete coupling delay and distributed coupling delay are studied respectively. For each kind of delay, Theproblem of synchronization under arbitrary switching is firstly studied,then for synchronization based on topology switching, the switching rulesare designed by using single Lyapunov and multiply Lyapunov functionmethods.3Synchronization of discrete switched network with delay in nodesthemselves is studied. Based on the single Lyapunov and multiplyLyapunov function methods, the synchronization criteria andcorresponding switching laws are obtained for nodes with both discreteand distributed delay.4Synchronization of discrete switched network with coupling delayis investigated. For discrete and distributed coupling delay, the problemof synchronization under arbitrary switching and synchronization basedon topology switching are studied respectively.