Qualitative Properties For Delayed Neural Networks Models On Time Scales

In this paper, by using the basic theory of time scale, we first consider the exis-tence of the periodic solutions of a delayed neural network model on a special timescale, then we consider the asymptotical properties of solutions of a class of dual-threshold delayed neural network model. Time scales can unify the discrete and con-tinuous dynamics cases. Therefore, it is important and has applications to study thequalitative properties of delayed neural networks on time scales.This paper consists of three chapters. The first chapter brie?y introduces thebackground, significance, major work of this paper and some basic theories of timescales which will be used in the paper.The second chapter studies the existence of periodic solutions of a delayedneural network model with one neuron when the transmission function is on a special time scale. According to the discontinuity of the sig-nal function, we get the existence of the periodic solutions and their asymptoticalstability of the neural network model by iteration.The third chapter focuses on the asymptotical properties of a dual-thresholddelayed neural network model when the transmission functions are . With regard to the three kinds ofthreshold values of the signal functions, we obtain different asymptotical propertiesof the model.