Studies On Stability Of Neural Networks With Delays

This thesis is divided into four chapters. In chapter one, we review the research background and developments of neural networks. Besides, we show it necessary to investigate the stability of neural networks with delays.In chapter two, we discuss the existence and global exponential stability of equilibrium point for three classes of Hopfield neural networks. In section two, we investigate the global exponential stability of a class of Hopfield networks with impulses and delays. Some results are obtained, which of them extend or improve the related results in previous literature. In section three, the stability of a class of delayed neural networks with inverse Lipschitz neuron activations is investigated by using the topological degree theory in connect with some analysis techniques. We obtain some new conditions ensuring the existence and global exponential stability of equilibrium. In section four, we consider the global exponential stability of Hopfield neural networks with two different neuron activations by means of the Lyapunov functional method. A new sufficient condition is given to guarantee global exponential stability of networks.In chapter three, we discuss the stability of two classes of neural networks with finite distributed delays. In section two, the global exponential stability of a class of neural networks with finite distributed delays is investigated by matrix measure technique and Halanay inequality. In section three, I present a class of neural networks with finite distributed delays and impulses based on the model in section two. The global exponential convergence of periodic solution of networks is investigated by constructing suitable Lyapunov function.In chapter four, we discuss the global dissipativity of a class of neural networks with finite distributed delays. Several sufficient conditions are given to guarantee global exponential dissipativity of the neural networks. These results play an important role in investigating the existence and stability or instability of equilibrium point for the similar networks and in investigating the existence of periodic solution for networks with finite distributed delays and extend the stability study of neural networks.