Convergence And Existence Of Periodic Solutions For Discrete-time Model Of Two-cell Cellular Neural Networks

Now well-known,discrete-time cellular neural networks(DTCNN) were first proposed by H.Harrer and J.A.Nossek in 1992,[15].Since then, they have been widely studied both in theorys and applications.They have been successfully applied imagnal porcessing,pattern recognition and associative memory.To date, most research on DTCNNs has restricted to the stability of a system[17-19,37,38].Few papers consider the existence and attractability of periodic so-lutions.Therefore,in this thesis, by using of the Lyapunov function ,Lasalle's in-variance principle and the analytical technique to construct return mappings[34-36],we describe some important properties of the dynamic behaviors of two class of discrete-time model of two-cell cellular neural networks ,which includes stability,asymptotic stability,the existence and attractability of periodic solutions. It is composed of three chapters.As the introduction,in Chapter l,the history and development of neural networks are reviewed briefly. The background of the model of cellular neural networks discussed in this thesis is interpretted and the problems to be resolved, the purpose and innovation of the investigation are denoted. Some useful notations and definitions are give in this chapter.In Chapter 2,a class of discrete-time model of two-cell cellular neural networks with symmetric temptate are investigated. We obtain some results about the stability,asymptotic stability,the existence and attractability of 2-periodic solutions.In Chapter 3,a class of discrete-time model of two-cell cellular neural networks with nonsymmetric temptate are investigated. We obtain some results that there is a Hopf-like local bifurcation of the equilibrium point in the origin and the coexistence of multiple attractive of 4k-periodic solutions besides the stability,asymptotic stability,the existence and attractability of 2-periodic solutions.Our results indicate that the dynamic behaviors of two models are very different.On the one hand,we have considered a case that a neuron may have self-...