Dynamic Behavior Analysis Of Several Classes Of Neural Network Models

In this thesis, we describe some important dynamic properties of a class of nonlinear neural network models of one neuron, obtain the sufficient conditions for the existence of the periodic solution of a class of discrete neural networks with three neurons, and study the dynamic of a general class of non-autonomous recurrent neural networks with variable coefficients and time-varying delays, which include uniformly ultimate boundedness, uniform boundedness, globally exponentially stable, and the existence of the periodic solution. It is composed of four chapters.In chapter 1, the background and history of neural networks are briefly reviewed, and the current situations in the field are generalized, furthermore, we raise some problems which will be investigated and list some notations which will be used in our paper.In chapter 2, a delay difference equation model of one neuron with piecewise constant nonlinearity is studied. Some interesting results are obtained for the asymptotic behavior of solutions of the equation, as well as the existence of periodic solutions.In chapter 3, we investigate the existence of periodic solution of a class of discrete neural network with three neurons, by using Lasalle's invariance principle and the analytical technique to find return mapping, we obtain the sufficient conditions for the existence of the periodic solutions.In chapter 4, the problems of boundedness and stability for a general class of non-autonomous recurrent neural networks with variable coefficients and time-varying delays are analyzed via employing Young inequality and Lyapunov method. Some simple sufficient conditions are given for uniform boundedness and uniformly ultimate boundedness for the solutions, as well as globally exponentially stable and the existence of the periodic solution for the neural networks. Two illustrative examples are given to demonstrate the effectiveness of our results.