Stability Of Periodic Solutions And Almost Periodic Solutions For Several Higher-order Neural Networks

In this thesis, we discuss some important properties of dynamic behaviors of several higher-order neural networks models with mixed delay, which includes the existence, uniqueness and exponential stability of the periodic solutions as well as almost periodic solutions.There are four chapters in this paper.As the introductions, in Chapter 1, the background of artificial neural networks and the development of Hopfield neural networks models are briefly addressed. We also introduce that higher-order neural networks are more prac-tical than one-order neural networks. The general knowledge of higher-order neural networks is introduced and the main work of this paper are given.In Chapter 2, we study the higher-order Hopfield neural networks with mixed delay and impulses: By using the continuation theorem of coincidence degree theory, differential inequality technique and constructing Liapunov functions,we derive the conclu-sion of the existence, uniqueness and global exponential stability of the periodic solutions of this neural networks, and cite an example to illustrate it.In Chapter 3, by using exponential dichotomy, the Banach fixed point theory, and differential inequality technique,some sufficient conditions are de-rived ensuring existence, uniqueness and global exponential stability of almost periodic solution for higher-order Hopfield-type neural networks with mixed de-lay.By using mathematical simulation, we prove the reasonability of our example according to our theorem.In Chapter 4, we discuss the competitive neural networks with mixed delay: By using exponential dichotomy, the Banach fixed point theory, and differential inequality technique, and introducing adjustable real parameter, we derive the sufficient conditions of the existence, uniqueness and global exponential stability of the almost periodic solutions of the competitive neural networks with mixed delay and different time scales.