概反周期函数及其在一类Hopfield神经网络上的应用  

ALMOST ANTI-PERIODIC FUNCTIONS AND THEIR APPLICATIONS ON A CLASS OF HOPFIELD NEURAL NETWORKS

作　　者：赵莉莉 赵霜 Zhao Lili;Zhao Shuang(School of Mathematics and Statistics,Yunnan University,650091,Kunming,China)

机构地区：[1]云南大学数学与统计学院,昆明650091

出　　处：《山东师范大学学报（自然科学版）》2024年第1期43-51,共9页Journal of Shandong Normal University(Natural Science)

基　　金：云南省教育厅自然科学基金资助项目(2020J0020)。

摘　　要：探讨一类具有混合时滞的中立型Hopfield神经网络的概反周期解的存在性与稳定性。首先,讨论了概周期函数与概反周期函数之间的关系,证明了全体概反周期函数构成的集合,是概周期函数空间的一个闭子空间。最后,利用不动点原理得到Hopfield神经网络存在一个唯一的有界解,而且该解函数还是概反周期函数。概反周期函数是比概周期函数更精细的函数,对神经网络概反周期解的存在性与唯一性的探讨,相较于对概周期解的存在性以及唯一性的探讨,能够更加精确地描述神经网络的动力学性质,所得结论是新颖的,是现有结论的进一步完善与补充。This paper is devoted to investigating the existence of almost anti-periodic solutions of a class of neutral Hopfield neural networks with mixed delays.Firstly,the relationship between almost periodic function and almost anti-periodic functions is discussed,and it is proved that the set of all almost anti-periodic functions is a closed subspace of the almost periodic function space.Finally,by using the fixed point principle,it is proved that the Hopfield neural network has a unique bounded solution,which is an almost anti-periodic function.Since the almost anti-periodic function is more precise than the almost periodic function,the discussion on the existence and uniqueness of the almost anti-periodic solution of neural networks can more accurately describe the dynamic properties of neural networks than the discussion on the existence and uniqueness of the almost periodic solution,the obtained conclusion is novel and serves as a further refinement and supplement to existing conclusions.

关 键 词：HOPFIELD神经网络 概周期函数 概反周期函数 BANACH空间 不动点原理 

分 类 号：O175.1[理学—数学]