Study On Spatiotemporal Chaos Synchronization Of Discrete Network

Synchronization of complex network is the one of the most active areas of complex network study at present. Since many complex phenomena in nature can be explained by synchronization of complex network, and it is closely contact with the real world, synchronization study of complex network has some practical significance and wide applications. The progress of complex network is recapitulative introduced in this thesis, including the establishment of complex network models, the features of network, the significance of network synchronization and research status at home and abroad. Meanwhile, two criterions of the synchronization of complex network, which are Master stability function criterion, Lyapunov function criterion are described, several typical reported examples of the complex network synchronization are also introduced. On this basis, A method is introduced to realize spatiotemporal chaos projective synchronization of weight network. The coupling function between connected nodes of the weight network is derived and the range of the linear coefficient matrix of separated configuration in state equation of the node is obtained through constructing a appropriate Lyapunov function. Bragg acousto-optical bistable system is taken as the local function, and unilateral coupled map lattices are taken as the spatial extend system to construct a laser spatiotemporal chaos model. Simulation is made to test the projective synchronization effect of the weighted network with the laser spatiotemporal chaos models as nodes. The results show that projective synchronization can be realized even if the coupling strength between the nodes is given arbitrary weight value. Further more, spatiotemporal chaos tracking synchronization of a complex network is studied. The structure of the coupling functions between connected nodes of the network and the range of the linear coefficient matrix of separated configuration in state equation of the node are obtained based on the control law designed by Milosavljevic. Complex network with a unilateral coupled map lattice as nodes is taken as an example to make simulation, in which an exponential map extended by a square map is taken as the local function. Simulation results show the effectiveness of the tracking synchronization principle.