Dynamics For Several Classes Of Infectious Disease Models And Neural Network Models

In this paper, we analyze the dynamical behaviors for three classes of infectiousdisease models and two classes of neural network models.This paper is divided into six parts.In the first chapter, it is introduced, the background and evolvement of stud-ding for infectious diseases models and neural network models.In the second chapter, the existence of positive solutions is studied for a classof SEIR model, and the final states of the solutions are analyzed. Moreover, somebiologic significance and numerical simulations are given.In the third chapter, the existence of positive solutions is analyzed for a class ofSEI model, and some conditions for local stability and global exponential stabilityare obtained by Lyapunov method, as well as, biologic significance is given.In the fourth chapter, the dynamic behavior of a class of SEI model with delayis studied. The stability of the equilibrium point, the Hopf bifurcation to delayparameters are analyzed through linear theory and Hopf bifurcation theory. Andthe bifurcation direction is analyzed through algorithm developed by Ruan andWei. In the end numerical simulations are given.In the fifth chapter, Using techniques developed by Kuznetson for discrete-time system, we study the stability of the equilibrium point and Hopf bifurcationfor a class of discrete-time BAM network model with three neurons.In the sixth chapter, we consider a class of Cohen- Grossberg neural networkswhere the neuron activations are modeled by discontinuous functions. By meansof the Lyapunov-like approach, a general result are proved on global exponentialconvergence toward a unique equilibrium point.