Global Stability Analysis For Several Classes Of Delayed Neural Networks

As an important part of delayed systems, the delayed neural networks may exhibit col-orful dynamical behaviors. Due to their important applications in signal processing, imageprocessing as well as optimizing problems, the dynamical issues of delayed neural networkshave attracted worldwide attention in recent years. This thesis mainly focuses on the sta-bility of two different kinds of delayed neural networks: distributed delays Hopfield neuralnetworks and time-varying delays Cohen-Grossberg neural networks. The global exponen-tial stability of Hopfield neural networks and with distributed delays and Cohen-Grossbergneural networks with time-varying delays are investigated in this thesis. To study neuronactivation functions of the above networks are Lipschitz continuous which have relaxed theusual monotonous activation functions, boundedness of the requirements and differentiabil-ity. In addition toIn addition, the weight matrices of the neural networks are need not tobe symmetric. depend on the definitions of global asymptotical stability and global robuststability, we mainly use homeomorphism principle as well as some mathematical analysistechniques, such as the way of contradiction, inequality techniques,etc. In the process ofresearch on the stability of the two different kinds of delayed neural network, Several novelglobal robust stability/global exponential stability criteria with less restriction are establishedby employing homeomorphism theory and Lyapunov functional method, our obtained cri-teria improves the existing result，some corresponding stability results are acquired, whichpossess some degree of novelty and representative.