| 引用本文: | 徐士国,肖敏,邱建龙,杨鑫松,黄创霞.高阶交互下具有环星型结构的分数阶时滞神经网络分岔[J].控制理论与应用,2026,43(1):12~21.[点击复制] |
| XU Shi-guo,XIAO Min,QIU Jian-long,YANG Xin-song,HUANG Chuang-xia.Bifurcation of fractional-order time-delayed neural network with ring-star structure under higher-order interactions[J].Control Theory & Applications,2026,43(1):12~21.[点击复制] |
|
| 高阶交互下具有环星型结构的分数阶时滞神经网络分岔 |
| Bifurcation of fractional-order time-delayed neural network with ring-star structure under higher-order interactions |
| 摘要点击 232 全文点击 38 投稿时间：2025-04-18 修订日期：2025-12-15 |
| 查看全文 查看/发表评论 下载PDF阅读器 HTML |
| DOI编号 10.7641/CTA.2025.50171 |
| 2026,43(1):12-21 |
| 中文关键词 神经网络 高阶交互作用 分数阶 Hopf分岔 |
| 英文关键词 neural networks higher-order interactions fractional-order Hopf bifurcation |
| 基金项目 国家自然科学基金项目(62073172),江苏省自然科学基金项目(BK20221329)资助. |
|
| 中文摘要 |
| 目前国内外关于神经网络分岔动力学研究主要集中于神经元间的二元交互,而神经网络中普遍存在神经
元间以群和组的形式发生的高阶交互作用.但是如今关于高阶交互作用对神经网络动力学的影响研究还不深入.
研究具有高阶交互作用的神经网络可以进一步探索真实神经网络中的高阶属性和动力学演化规律.为此,本文提出
了一类高阶交互下具有环星型结构的分数阶时滞神经网络模型.选取时滞作为分岔参数,给出系统的稳定性
和Hopf分岔的充分条件,揭示高阶耦合系数、自反馈系数和分数阶次对系统动力学的影响机制. |
| 英文摘要 |
| Currently, studies on the bifurcation dynamics of neural networks mainly focus on the binary interactions
between neurons, while higher-order interactions between neurons in the form of groups and clusters are common in neural
networks. However, the effect of higher-order interactions on the dynamics of neural networks is not well understood. The
study of neural networks with higher-order interactions can further explore the higher-order properties and dynamics of real
neural networks. In this paper, we propose a class of fractional-order time-delayed neural network with ring-star structure
under higher-order interactions. The time delay is chosen as the bifurcation parameter, and the stability of the system and the
sufficient condition for Hopf bifurcation are given, which reveals the mechanism of the higher-order coupling coefficient,
the self-feedback coefficient and the fractional-order on the system dynamics. |
|
|
|
|
|