The Pseudo Almost Periodic Solutions Of Two Classes Of Neural Networks

The paper consists of three parts: the first part concerns on the proof of the equivalent definition of almost periodic type functions. Since the Danish mathematician H. Bohr developed the theory of almost periodic functions in the 1920s, the theory has been improved greatly by the hardworking of many mathematicians for decades. Almost periodic functions have many perfect characters.In this paper, we mainly introduce the invariant mean and the almost periodicity of composited function as an arrangement necessary for the existence of the solution of almost periodic type differential equation .The second part concerns of the solutions of almost periodic type differential equations. In the study of the characters of almost periodic type differential equation, we use exponential dichotomy which is a powerful tool to prove the exsitense of the solution .The last part concerns on the two important classes of artificial neural nets and the exsitence and stabilities of their solutions. In this paper, we generalized the almost periodic type solution to the pseudo almost type ones, and use the method of analysis of inequliaties and Liapunov function to prove the stabilites of the solutions. Shunting inhibitory neural networks (SICNNs) and the Hopfield neural network (HNNs) in signal, image processing, associated memory, pattern recognition have important applications. A lot of papers in these two neural networks present many conclusions about the almost periodic characters of the solutions, but there is few papers concerns about the pseudo almost periodic solution yet. In this paper, we have studied the pseudo almost periodic solutions of the two classes of neural net works and their stabilities. When prove the existence of the solutions, we construct a contruction map and the solution is its fixed piont. The past conclusions are included in the new ones.