Global Synchronization Analysis Of Several Coupled Complex Dynamical Networks With Time-delays

Based on some existing works, this thesis is devoted to the study of globalsynchronization for several delayed complex dynamical networks by means of Lya-punov functional, linear matrix inequality and some other skills. some su?cientconditions are obtained to guarantee the synchronization of the considered systems.The paper is composed of three chapters.In the first chapter, the background and history of neural networks are pre-sented. Then, several relevant literatures of neural network models are reviewed.Furthermore, the main work of this paper is simply introduced.In the second chapter, firstly attention is paid to the global asymptoticallysynchronization of a mixed-delay dynamical network model. By means of the Lya-punov functional, linear matrix inequality and some other skills, some su?cientconditions are derived. These conditions are expressed in terms of LMIs, and canbe checked by resorting to the Matlab LMI toolbox. secondly, dropping o? thesymmetry, irreducibility and di?usive coupling connection of the coupling matrix,we obtain a su?cient condition ensuring global exponentially synchronization of theconsidered model. And then we study the global asymptotically and exponentiallysynchronization of another coupled dynamical networks model with distributed de-lay, similarly several su?cient conditions are deduced. At last, numerical examplesare provided.In the third chapter, the asymptotic behaviors of the complex dynamical net-works modelled by a di?erence equation form are discussed. By using the classicalanalysis technique, we get a su?cient condition for its global synchronization.