Analysis Of A Class Of Neutral Three Neurons Network With Delay

In this paper, the stability and bifurcation of a class of neutral three neurons network model is studied. This paper has three main topics:the stability of equilibrium points, the existence and direction of bifurcation, and the existence of permanent oscillation. In the process of analysis model, zero distribution theory of transcendental function and Hopf bifurcation theory of dynamical systems has been widely used. The main work is as follows:In the first part, seven kinds connections of the three neurons is introduced and analyzed. And we also give the corresponding characteristic equation of linearization neutral three neurons network modelIn the second part, as an Example in one connection, in the neutral three neurons network modelWe discuss the stability of equilibrium point (0,0,0) and the extension of local Hopf bifurcation of neutral three neurons network model..In the third part, the stability and properties of the Hopf bifurcation are discussed by applying the normal form method and the center manifold theorem.In the fourth part, As an Example in a connection, in the neutral three neurons network modelIn the fifth part, We discuss the existence of permanent oscillation.In this paper, we make a rigorous proof in theory and carry out a large number of numerical simulations on the model respectively in article IV to support the analytic result. The results not only have a high theoretical significance for the neural network, but also have a good reference value.