Study On Synchronization Between Complex Network And External Signals

Researches on complex network started from the 20 th century.In recent years,the improvement of Internet technology directly accelerates the trend of global networking process,it also makes researches on complex network achieve to the climax.A great number of researchers major in physics,biology engineering and computer science are devoting themselves to this realm.At present,researches on complex network are mainly focusing on network characteristics,network modeling and network dynamics.Among these studies,the synchronization and control issues of complex network which under the field of network dynamics have been deeply studied due to their important potential in laser network,neural network,secret communication and so on.In this thesis,the synchronization issue of a network and external signals is studied.In the first chapter,the complex network is introduced including its history,definition,basic concepts,topological models and applications.In the second chapter,the definition of network synchronization,different types of network synchronization,criterion of synchronization and sliding mode control technique are presented.In the third chapter,by using the sliding mode control method,the neural network which has a small-world effect gets synchronized with its external signals which have different structures.Based on Lyapunov stability theorem,the sliding mode surfaces and the controller which has an uncertain configuration coefficient are both designed to realize the synchronization,also the uncertain configuration coefficient can be effectively configured.Later on,a sinusoidal signal and a node of FitzHugh–Nagumo neural network are applied in the numerical simulation part.In the forth chapter,the synchronization issue of a discrete cluster network with external signals is studied,by using the Lyapunov stability theorem,the Lyapunov function is designed as an adjustable positive function,it is also in form of error and includes an adjustable uncertain coefficient.By adjusting the coefficient,the synchronization of a discrete spatio–temporal cluster network with external signals can be realized.Also the uncertain coefficient can be discerned by using the adaptive law.In the simulation part,Coupled map lattice(CML)and Generalized logistic system are not only chosen as the node's function in different clusters but also the signals' function,the validity of our design is proved at the same time.