Qualitative Analysis Of A Class Of Neural Network Model With Two Neurons

In this paper, we analyze the dynamical behaviors of solutions for a class of neural network model with two neurons. And the signal transmission function is three piecewise constant discontinuous.For the neural network model with delay, the state equation with the synaptic transmission delay is transformed into ordinary differential equation by means of the step method. Then the dynamical behaviors of the model can be studied by analyzing the solutions of the ordinary differential equations. Considering the change of the threshold, the values of the thresholds in the model are divided into three parts. In each condition, since the signal function is three piecewise constant discontinuous, the scope of the initial value can be subdivided into nine cases. Combining the transformation of the threshold, the solutions are obtained in every identical space. We discuss the solutions with different initial values in every part. And it can be judged whether the solutions are convergent or periodic.The paper has four parts.In the first chapter, the background and the necessity for the study of neural networks are presented. Then, some known results of neural network models are introduced. And the main work of this paper is also simply introduced.In the second chapter, the asymptotic behaviors of the solutions are studied when the two thresholds are bigger than 1. And it is found that the solutions of the model are convergent on most conditions.In the third chapter, the asymptotic behaviors of the solutions are discussed when one threshold is bigger than 1 but the other one is less than 1. It is proved that the solutions of the model are convergent on most conditions.In the fourth chapter, some important dynamic properties of the models are described when the two thresholds are less than 1. It is proved that the solutions of the model are convergent on most conditions, and on some suitable conditions, such a model has periodic solutions.