Order Neural Network Dynamic Behavior

This paper studies the dynamic behavior of certain typical high-order neural network models. Through the application of the Young's inequality, we obtained some sufficient conditions to ensure the existence of the model's equilibrium or periodic solution without assuming the boundedness of signal transmission functions. In addition, by using some inequality analysis techniques and constructing suitable Lyapunov function, only under the bound condition to high-order signal transmission functions, some sufficient criterions which ensure the global exponential stability of equilibrium or periodic solution are established.The paper is composed of four chapters.In chapter 1, we will review the development of artificial neural network history and introduce the biological basis of high-order neural networks, moreover, the studying status quo on high-order neural networks and its research significance are summarized systematically.In chapter 2, we research the existence and global exponential stability of equilibrium for high-order Cohen-Grossberg neural networks.In chapter 3, the existence, uniqueness and global exponential stability of equilibrium for high-order BAM neural networks with time delays are discussed.In chapter 4, some sufficient theorems are obtained for ensuring the existence and global exponential stability of periodic solution to high-order BAM neural networks with time-varying delays.