The Stability And Hopf Bifurcation Of Neutral-type Neural Network Model

Neural network model is the mechanism of information transmission and processing of biological neural networks,artificial design and synthesis of a simulation system.Some parameters of the system,such as: the weights of synaptic connections,neuron threshold and time delay,etc.These parameters may affect the dynamics properties of the neural network system,so,it is significance to consider the bifurcation of neural network system.In this paper,we consider the stability and Hopf bifurcation of neutral-type neural network model.The first part,we consider the dynamic behavior of neutral neural network model with two time delays.Firstly,the conditions to ensure the local stability of the trivial solution and the existence of Hopf bifurcation of the system are investigated by choosing t₁ and t₂ as parameters,respectively.Then the properties of local Hopf bifurcation is discussed by using the center manifold theory and normal form method.Finally,several numerical simulations are carried out to illustrate the theoretical analytical.The second part,we investigate the neutral neural network model with discrete and distributed delays.Firstly,by analyzing the distribution of the root of exponential polynomial equation,a sufficient condition for the existence of the local Hopf bifurcation of the system is given by choosing t₁ and t₂ as parameters,respectively.Then,we consider the global existence of the periodic solution by using the global Hopf bifurcation theory.Finally,some numerical simulations are given to illustrate the analytical results.