Stability And Bifurcation Of A Three-Dimension Discrete Neural Network Model

In this paper, an in-depth research on the stability and bifurcation of a three-dimension discrete neural network model is made in this thesis. On the one hand, a three-dimension discrete neural network model without delay is considered. On the other hand, a three-dimension discrete neural network model with delay is considered. Bifurcation theory on Discrete Dynamic System and Extensional Jury Criterion are extensively applied in this thesis. The main tasks are as follows.In the first part, ten kinds of connection in the three neurons are considered. And we also give the corresponding characteristic equation of linearization discrete neural network model.In the second part, we investigate the stability and bifurcation of a three-dimension with single-directional fully connected discrete neural network model without delay (with self-feedback) We discuss the asymptotically stability on equilibrium, the existence of Neimark-Sacker bifurcation and the bifurcation direction.In the third part, we discuss the stability and bifurcation of a three-dimension with fully connected discrete neural network model with delay (with self-feedback) k is the time-delay. We discuss the asymptotically stability on equilibrium, D₃-equivariant and the existence of multiple periodic solutions and the bifurcation direction.In the fourth part, we investigate the stability and bifurcation of a three-dimension with non-fully connected discrete neural network model with delay (with self-feedback) k is the time-delay. It is also using the same method with the third part and obtains some relevant results. This paper makes strict theory proof and gives concrete computer simulation experiments. Not only do our experimental results illustrate the stability and bifurcation of a three-dimension discrete neural network model without delay and with delay, but also can be easily implemented in actual systems. Finally, computer simulations are performed to support the theoretical predictions.