| In the realization of the artificial neural networks, the propagation delay is inevitable because the signal transmission speed is limited, As a result, when we study the neural network for qualitative analysis, considering the impact of time delay is very important. This paper mainly studies that Cohen and Grossberg jointly create Cohen-Grossberg neural network model in 1983. The stability of two kinds of Cohen-Grossberg neural network model with multi-delays are analyzed, the main content as follow:In chapter 1, we introduce the background and significance of the subject.The development history and research status of the Cohen-Grossberg neural network model is introduced.In chapter 2, a kind of discrete Cohen-Grossberg neural network model with multi-delays are investigated. The stability and bifurcation of equilibrium points of the mode mainly are studied. Based on the existing results, conditions of the asymptotic stability of the equilibrium point are given. In addition, values of parameters are discussed in detail. The results show that the system produces Neimark-sacker bifurcation, fold bifurcation and flip bifurcation in a certain parameter values. In addition, bifurcation of codimension 2, for example, fold-Neimark-sacker bifurcation, Neimark-sacker bifurcation and flip-Neimark-sacker bifurcation of double also can produce. The results show that the discrete Cohen-Grossberg neural network model with multi-delays has the rich dynamicsIn chapter 3, a kind of Cohen-Grossberg neural network model with multi-delays is investigated. The mainly research is that the change of delay influence on the stability of equilibrium point of the model. By the analysis of the corresponding characteristic equation, the sufficient condition of locally asymptotically stable equilibrium point is given for different delay parameters. In addition, it is shown that the stability switches for time delays, and Hopf bifurcation may occur within certain range of the model parameters. |
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