Research On The Existence Of Solutions For Several Classes Of Neural Network Systems

In this thesis, by using degree theory, fixed point theory and stability theory, we consider the existence and stability of solutions (such as periodic solutions, almost periodic solutions, anti-periodic solutions and weighted pseudo almost periodic solutions) for several classes of neural network systems.The main organization as follows:In Chapter 1, we introduce some backgrounds for several classes of neural networks, the main works of this thesis and some basic theory.In Chapter 2, we mainly study a class of neutral cellular neural networks with dis-tributed delays. Firstly, we introduce some basic knowledge of degree theory. Secondly, by using the abstract continuation theorem of k-set contractive operator and inequality techniques, some sufficient conditions for the existence of periodic solutions are obtained.In Chapter 3, we discuss a class of neutral Hopfield neural networks with distribut-ed delays. Firstly, we introduce the basic theory and the properties of almost periodic functions. Secondly, we get some sufficient conditions for the existence of almost period-ic solutions by using Banach fixed point theorem. Finally, by applying the definition of stability, it is shown that the almost periodic solution is global exponential stable.In Chapter 4, we consider a class of high-order Hopfield neural networks (HHNNs) with delays and impulses. Sufficient conditions for the existence and global exponential stability of anti-periodic solutions are established by using Krasnoselskii’s fixed point the-orem, Lyapunov function method and inequality techniques, and then an example and numerical simulations are given to illustrate our main results.In Chapter 5, we investigate dynamics of 2N weighted pseudo almost periodic solu-tions for cellular neural networks (CNNs) with variable and distributed delays. Firstly, we split the invariant basin of CNNs into 2N compact convex subsets. Then by applying Banach fixed point theorem and inequality techniques, we obtain the system has at least one weighted pseudo almost periodic solution in every compact convex subset. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.