| In this paper,the BAM neural networks with discontinuous activations and mixed time delays are investigated.Under the framework of the Filippov solution,combining differential inclusion theory and set-valued mapping theory,by constructing suitable Lyapunov functionals and applying appropriate inequality,the global dissipativity of the considerded BAM neural networks has been analyzed,and several sufficient conditions that easy-to-test are obtained.In addition,different controllers are designed to study the synchronization problem of the system,and sufficient conditions are obtained to ensure the synchronization of the system.Finally,based on Matlab programming,the rationality and validity of the obtained results have been demonstrated by numerical simulations.The full text is divided into five chapters.Chapter 1 is the introduction part,which briefly summarizes the research status of BAM neural networks,memristor-based neural networks and fuzzy neural networks.In Chapter 2,the global dissipativity of a class of BAM neural networks(BAMNNs)with discontinuous activations and mixed time delays are studied.First,the existence of the solution is proved according to the Continuation Theorem and Gronwall inequality.Then,by constructing Lyapunov functional and emplying a generalized Halanay inequality,some sufficient conditions for ensuring the global dissipativity of the considered BAM neural networks are proposed.In Chapter 3,the general decay synchronization(GDS)of memeristor-based BAM neural networks(MBAMNNs)with discontinuous activations and mixed time delays is inveatigated.Based on the definitions of ?-type function and ?-type stability,we firstly given the definition of general decay synchronization.Then,two different types of controllers,adaptive and non-adaptive,are designed to study the general decay synchronization of the system.In Chapter 4,the fuzzy terms are added to the BAM neural networks,and a novel fuzzy BAM neual networks(FBAMNNs)with discontinuous activations and mixed time delays are studied.By designing time-independent and time-dependent,two different types of nonlinear controllers,sufficient conditions are obtained to ensure the general decay synchronization of the system.Chapter 5 is a summary of the whole work of this paper,and the developing directions that needs to be further explored in the future are pointed out as well. |
