The Stability And Bifurcation Of Equilibrium Point Of Discrete Neural Network Models

The stability of the equilibrium point and bifurcation for a kind of discrete neural network model is concerned in this thesis. The thesis contains five chapters.As the introduction, in Chapter 1, the develop background and research status of discrete neural networks model are briefly addressed, and some notations and definitions are given in this thesis.The stability of the equilibrium point and Neimark-Sacker bifurcation for discrete neural networks of two,four neurous are studied in Chapter 2,3, respectively. The calculating formulae of direction and stability of the bifurcation are obtained by using the normal form theory and the center manifold theorem. By using the mathematical software of Matlab, results of thesis are displayed graphically which show the validity and feasibility of the theory.In Chapter 4, we discussed a kind of three neurous delay discrete neural networks model. By using the skill of mathematical analysis, we analysis the characteristic roots of corresponding linearization system and obtain local stability of the equilibrium point and bifurcation point. Choosing an appropriate bifurcation parameter, the stability of the equilibrium point, Pitchfork/Flip/Neimark-Sacker bifurcation are discussed. We obtained the calculating formula of direction by using the center manifold theorem.In Chapter 5, we summarized the main results of this thesis and further research direction of the discrete neural networks model.