摘要
自一类特殊的微分方程即带有延迟的细胞神经网络被建立以来,讨论其各种解的存在性和唯一性成为重要研究内容,特别是对概周期型解的研究。为了探讨渐近概周期函数在一类带可变延迟细胞神经网络中的应用,依据Banach不动点定理和指数二分法的有关知识,并结合已有文献对这类细胞神经网络概周期解的研究,讨论了这类细胞神经网络的渐近概周期解的存在及唯一性问题,证明了该类方程在一定的充分条件下有唯一的渐近概周期解。
Since a class of specific differential equations called cellular neural networks with delays have been established,the discussion on existence and uniqueness of all kinds of solutions for this class of equation become important study contents,especially the study on almost periodic type solutions. In order to study asymptotically almost functions,applications on a class of cellular neural networks with varying delays, the existence and uniqueness of asymptotically almost periodic solutions on this class of cellular neural networks are discussed by using Banach fixed point theorem and some knowledge on exponential dichotomy,combining with the research of almost periodic solutions on this class of cellular neural networks in some literature,and it is proved that this class of cellular neural networks has unique asymptotically almost periodic solution under some sufficient conditions.
出处
《哈尔滨理工大学学报》
CAS
北大核心
2017年第5期130-136,共7页
Journal of Harbin University of Science and Technology
基金
黑龙江省教育厅科学技术研究项目(12511110)
关键词
细胞神经网络
渐近概周期解
指数二分法
不动点
延迟
cellular neural networks
asymptotically almost periodic solutions
exponential dichotomy
fixed point, delay
