Stability Analysis For A Class Of Delayed Impulsive Neural Networks

As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dy-namical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums of delayed neural networks with impulses have been derived via Lyapunov function/functional method. A series of significative results have been obtained. This thesis mainly focuses on the global stability for a type of delayed neural networks with impulse. Specifically, the main contents are as follows:(1) Non-Lipschitz Neuron Activations for Delayed Neural Networks with ImpulsesMost existing results on stability for neural networks with impulses were obtained under some special assumptions on neuron activation functions, such as Lipschitz conditions. Cor-respondingly, there is not much work dedicated to investigate the stability of neural networks with non-Lipschitz neuron activations. The objective of this thesis is to study the stability of a class of delayed impulsive neural networks with non-Lipschitz neuron activations. Our results obtained in this thesis provide new sufficient criteria for a class of delayed impulsive neural networks developed by us.(2) Stability Analysis for Delayed Neural Networks with ImpulsesSeveral novel global asymptotical stability/global exponential stability criteria with less restriction are established by employing homeomorphism theory, topological degree theory and Lyapunov functional method, our obtained criteria improves the existing result.(3) Effects of Impulses on Stability of Delayed Neural NetworksWe investigate the global stability conditions of the delayed neural networks with im-pulses by means of inequality techniques. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse inter-val can be estimated by applying the proposed results.