Global Stability Analysis For Two Classes Of Delayed Neural Networks

As an important part of delayed large systems, the delayed neural networks may exhibitcolorful dynamical behaviors. This thesis mainly focuses on the global stability of two differ-ent kinds of delayed neural networks: delayed Hopfield neural networks and delayed BAMneural networks. The global exponential stability of Hopfield neural networks and BAMneural networks with constant delays and distributed delays are investigated in this thesis. Inaddition, the global uniformly asymptotical stability of Hopfield neural networks with dis-tributed delays is also studied. Our consideration of neuron activation functions of the abovenetworks are Lipschitz continuous which have relaxed the usual requirements of monotonic,differentiable, bounded on activation functions. Besides, the weight matrices of the neuralnetworks are not assumed to be symmetric. Beginning with the definitions of global ex-ponential stability and global uniformly asymptotical stability, we mainly depend on con-traction mapping principle and some mathematical analysis techniques, such as inequalitytechniques, by the way of contradiction, mathematical induction, etc., some correspondingstability results are acquired, which possess some degree of novelty and representative. Inthe studies of global stability of these neural networks, some of them only need to constructsimple Lyapunov functions, and some of them totally unnecessary to construct Lyapunovfunctions. We are no need to make great effort to construct suitable Lyapunov functions forcomplex systems. In fact, these are difficult.