Study On Projective Synchronization Of Irregular Networks

The synchronization study of complex network always is a concern issue. In our life, theeffect and the value of synchronization study should not be under estimated. At present, thescholars of the domestic and foreign have devoted to research the synchronization of complexnetworks, and they have made remarkable achievements in synchronization research. On thebasis of previous foundation works, this thesis does a preliminary exploration about thesynchronization of the small world network and scale-free network.First of all, the development history of complex network is introduced in the thesis. Andthen, the basic concept, types, characteristics and application status are summed up generally.The point that the synchronization of complex network is an important application in thetheory of complex network is further expounded. In the second part, the theory, concept andjudgment rules for the synchronization of complex dynamic network are explained specifical-ly, and the complete synchronizations of the regular network, small world network andscale-free network are discussed. In the third part, coupled projective synchronization of thesmall world network is emphasized and studied. Base on Lyapunov theorem, the range of thecoupling strength and unknown parameters is determined, and the Logistic nonlinear chaoticsystems are selected as the nodes of network which is an example of this issue. Thoughnumerical simulation, the coupled projective synchronization between the small worldnetwork and objective system is achieved well and the change of the projection parameter isnot influence on the experimental results. On the basis of it, the research is extended in thisthesis to realize the synchronization between the scale-free networks. On the basis ofLyapunov theorem, the structure of the controller is designed. The unknown parameters kiinthe controller are identified and the parameters γiof the Lipschit condition are adjusted thoughdesigning reasonable control input. At last, the Van der Pol equations are chosen as the nodesof network to exhibit the example of this issue. It can be known from the figures of numericalsimulation that the projective synchronization between two networks is achieved well.