Local Stability And Attractive Basin Of Cohen-Grossberg Neural Networks With Time Delay

In the realization of the process of the artificial neural networks, the prop-agation delay is inevitable. Because in the absence of time delay and the globalasymptotic stability of neural networks, there will occurred oscillation after theintroduction of time-delay. As a result, when we study the network for qualitativeanalysis, considering the impact of time delay is very important, this also arousedwide attention from scholars at home and abroad.The most common of the Cohen-Grossberg neural network model in parallelprocessing, associative memory, in particular the optimization calculations have awide range of applied research, a lot of literature introduced delay Cohen-Grossbergneural network model for the global asymptotic stability or exponential stabilityproblem, and gives a guarantee for global asymptotic stability or exponential sta-bility for some su?cient conditions. As for the local stability ,there are few peopleto get involved. In this case, this article tries to take the Cohen-Grossberg neuralnetworks with regular time-delay and the Cohen-Grossberg neural networks withcontinuously distributed delays solutions for exploring the local convergence, equi-librium point has been reached its local stability and local exponential stabilityin some su?cient conditions, and the estimation of size of the attraction basin.Then sum up an important conclusion, Assuming that the conditions are fulfilled,the su?cient conditions for local stability of the Cohen-Grossberg neural networkswith regular time-delay apply to the Cohen-Grossberg neural networks model withcontinuously distributed delays.This thesis is composed of three chapters.In the first chapter, we introduce the historical background of problems whichwill be investigated and the main works of this paper. For convenience of expres-sions, we also introduce some notations which will be used in this thesis.In the second chapter, we discuss the local stability and local exponentialstability of the Cohen-Grossberg neural networks with regular time-delay under twodefinitions of the norm. By constructing a Lyapunov function and the applicationof some techniques, such as inequality, we get some su?cient conditions for theequilibrium point of the model to achieve local stability, and these conditions areindependent of the delay. In the third chapter, we discuss the local stability and local exponential stability ofthe Cohen-Grossberg neural networks with continuously distributed delays undertwo definitions of norm. we get some su?cient conditions for the equilibrium pointof the model to achieve local stability. These conditions are not only independentof the delay, but also similar to the conditions of the Cohen-Grossberg with regulartime-delay. It is an important conclusion gained in this paper.The end is conclusion and summing up the full text, and point the directionof future research.