一类二元离散时滞细胞神经网络模型的周期解的存在性

Convergence and Existence of Periodic Solutions for a Class of Discrete time-delay Model of Two Cellular Neural Networks

人工神经网络是人工智能的一个重要分支,在现代控制理论中有着十分重要的作用.迄今为止,众多研究者对此进行了大量的研究,建立了如Hopfield、BMA等许多模型,但是从数学的角度对这些模型的动力学行为的研究缓慢,导致其动力学行为没有得到充分的揭示,特别是对离散的神经网络模型的动力学行为的定性研究成果尤其更少.为此,本文利用时滞差分方程的有关理论及周期解的概念,讨论了一类二元离散时滞细胞神经网络模型的周期解的存在性,探讨了其动力学行为,相关结论可为大规模网络的研究和设计提供借鉴的方法.

Artificial neural network is an important branch of artificial intelligent, which plays a curious roll in the advanced control system. Up till now, scholars have carried out a lots of research about this network, and obtained many famous models, such as Hopfield,BMA, and so on. But the research process of the model＇s dynamic characteristics through the mathematic methods was very slow, so the neural network＇ s dynamic behaviors has not been fully revealed, especially about the discrete-time networks model. So in this paper, by using of relevant theories of the time-delay differential equation and its periodic solution concept, the paper discussed the existence of periodic solutions of a class of delay discrete-time networks model with two-cell cellular neural , and the conclusion is beneficial to the research of the large -scale network.