时标上的Clifford值概周期函数与动力方程的Clifford值概周期解  

Clifford Valued Almost Periodic Functions on Time Scales and Clifford Valued Almost Periodic Solutions of Dynamic Equations

作　　者：赵莉莉 ZHAO Lili(School of Mathematics and Statistics,Yunnan University,Yunnan Kunming 650091,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650091

出　　处：《河北师范大学学报（自然科学版）》2024年第1期19-28,共10页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11861072);云南省教育厅自然科学基金(2020J0020)。

摘　　要：为了更好地在时标上探讨Clifford值神经网络概周期解的存在性,首先,从周期时标的定义出发,利用Clifford代数空间的完备性,给出时标上Clifford值概周期函数的定义,并讨论了这类函数的相关性质.其次,通过证明时标上Clifford值右稠密连续函数空间的完备性,以及时标上Clifford值概周期函数空间是时标上Clifford值右稠密连续函数空间的闭子空间,获得时标上Clifford值概周期函数空间的完备性.最后,利用时标上Clifford值概周期函数相关性质,得到一阶动力方程Clifford值概周期解的存在性定理.In order to discuss the existence and stability of almost periodic solutions of Clifford-valued neural networks on time scales,firstly,the definition of Clifford valued almost periodic functions on time scales is given based on the definition of periodic time scales and the completeness of Clifford algebraic space,and the related properties of these functions are discussed.Secondly,the completeness of Clifford valued almost periodic functions space on time scales is obtained by proving that the space of Clifford valued right dense continuous functions on time scales is complete and that the space of Clifford valued almost periodic functions on time scales is a closed subspace of the space of Clifford valued right dense continuous functions on time scales.Finally,by using the properties of Clifford value almost periodic function on time scale,the existence theorem of Clifford value almost periodic solution of the first order dynamic equation is obtained.

关 键 词：CLIFFORD代数 神经网络 时标 概周期函数 全局指数稳定性 

分 类 号：O175.1[理学—数学]