The Stability Analysis Of Delayed Neural Networks

This dissertation present some qualitative studies on several neural networks models withdelay which includes globally asymptotic stability, globally exponential stability, chaos synchro-nization, multiperiodicity attractivity. All the context can be divided as 5 chapters. We generalizethe content as following:(i) Utilizing Linear matrix inequality theory, Lyapunov functional, M-matrix theory, westudy the globally asymptotic stability and globally exponential stability of Cohen-Grossberg neu-ral networks with time-varying delays and distributed delays. The obtained results consider thefunction of input vector in the stability analysis which is ignored in previous work. The presentedcriteria have more general applications.(ii) Based Lyapunov functional, Linear matrix inequality and nonsmooth analysis theory,we study the globally asymptotic stability and chaos synchronization of a general class of neuralnetworks. Under the assumptions without demanding the boundedness of activation functions, weobtain some new results concerning the existence uniqueness and globally asymptotic stability ofequilibrium points of the neural networks with time-varying delays. Meanwhile, we propose a newtheme for the chaos synchronization of a class of chaotic neural networks.(iii) Under the conditions fully considering the characteristic of activation functions of cel-lular neural networks, we first propose the criteria about the multiperiodicity and multistability ofhigh order cellular neural networks and cellular neural networks described by cloning templates.The obtained results are totally new in the studied neural networks which have a great significantinspiration in the theoretical analysis of neural networks.