Synchronization of coupled heterogeneous complex networks

By only designing the internal coupling, quasi synchronization of heterogeneous complex networks coupled by N nonidentical Duffing-type oscillators without any external controller is investigated in this paper. To achieve quasi synchronization, the average of states of all nodes is designed as the virtual target. Heterogeneous complex networks with two kinds of nonlinear node dynamics are analyzed firstly. Some sufficient conditions on quasi synchronization are obtained without designing any external controller. Quasi synchronization means that the states of all nonidentical nodes will keep a bounded error with the virtual target. Then the heterogeneous complex network with impulsive coupling which means the network only has coupling at some discrete impulsive instants, is further discussed. Some sufficient conditions on heterogeneous complex network with impulsive coupling are derived. Based on these results, heterogeneous complex network can still reach quasi synchronization even if its nodes are only coupled at discrete impulsive instants. Finally, two examples are provided to verify the theoretical results.