Weyl almost automorphic solutions for a class of Clifford-valued dynamic equations with delays on time scales
Weyl almost automorphic solutions for a class of Clifford-valued dynamic equations with delays on time scales
复制标题
一类时标时滞的 Clifford 值动态方程的 Weyl 几乎自守解
DOI：
10.1002/mma.8575
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发表时间：
2022
影响因子：
2.9
通讯作者：
Xiaoli Huang
中科院分区：
文献类型：
--
作者：
李永昆;Xiaoli Huang
Weyl几乎自同构是Bochner几乎自同构和Stepanov几乎自同构的自然推广。然而，由Weyl几乎自同构函数组成的空间不是Banach空间。因此，关于微分方程解的 Weyl几乎自同构解的存在性的结果很少，差分方程组的 Weyl几乎自同构解的存在性的结果也很少。由于时间尺度上的动力学方程的研究可以统一于微分方程组和差分方程组的研究。因此，本文首先提出了时间尺度上的 -Weyl几乎自同构函数的概念，然后以时间尺度上具有时变时滞的Clifford值并行抑制细胞神经网络为例，研究了其Weyl几乎自同构解的存在性和全局指数稳定性。我们还给出了一个数值例子来说明我们结果的可行性。
Weyl almost automorphy is a natural generalization of Bochner almost automorphy and Stepanov almost automorphy. However, the space composed of Weyl almost automorphic functions is not a Banach space. Therefore, the results of the existence of Weyl almost automorphic solutions of differential equations are few, and the results of the existence of Weyl almost automorphic solutions of difference equations are rare. Since the study of dynamic equations on time scales can unify the study of differential equations and difference equations. Therefore, in this paper, we first propose a concept of Weyl almost automorphic functions on time scales and then take the Clifford‐valued shunt inhibitory cellular neural networks with time‐varying delays on time scales as an example of dynamic equations on time scales to study the existence and global exponential stability of their Weyl almost automorphic solutions. We also give a numerical example to illustrate the feasibility of our results.