具有时变时延与状态依赖切换的分数阶 Cohen-Grossberg 神经网络的多稳定性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2418-2432.

具有时变时延与状态依赖切换的分数阶 Cohen-Grossberg 神经网络的多稳定性

董红勋¹(), 万里光¹^,^*(), 吴爱龙²()

¹ 湖北师范大学电气工程与自动化学院湖北黄石 435002
² 湖北师范大学数学与统计学院湖北黄石 435002

收稿日期:2025-04-14 修回日期:2025-06-23 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 万里光 E-mail:dhx3324@163.com;wanliguang@hbnu.edu.cn;hbnuwu@yeah.net
作者简介:董红勋, E-mail: dhx3324@163.com;
吴爱龙, E-mail: hbnuwu@yeah.net
基金资助:
湖北省自然科学基金(2024AFB837);国家自然科学基金(62476082);湖北省教育厅科研计划指导项目(B2023133)

Multistability of Fractional-Order Cohen-Grossberg Neural Networks with Time-Varying Delays and State-Dependent Switching

Hongxun Dong¹(), Liguang Wan¹^,^*(), Ailong Wu²()

¹ School of Electrical Engineering and Automation, Hubei Normal University, Hubei Huangshi 435002
² School of Mathematics and Statistics, Hubei Normal University, Hubei Huangshi 435002

Received:2025-04-14 Revised:2025-06-23 Online:2026-12-26 Published:2026-08-14
Contact: Liguang Wan E-mail:dhx3324@163.com;wanliguang@hbnu.edu.cn;hbnuwu@yeah.net
Supported by:
NSF of Hubei Province(2024AFB837);NSFC(62476082);Guiding Project of Scientific Research Plan of Hubei Provincial Department of Education(B2023133)

摘要/Abstract

摘要：

该文主要研究具有时变时延与状态依赖切换的分数阶 Cohen-Grossberg 神经网络 (SFCGNNs) 的多平衡点的共存性与稳定性. 利用状态空间划分的方法获得 SFCGNNs 具有 $5^n$ 个平衡点的存在性. 为了证明其中 $3^n$ 个平衡点是渐近稳定的, 采用 Lyapunov 方法, 此外还给出其余平衡点不稳定的充分条件. 最后通过两个数值算例验证结果的有效性.

关键词: 多稳定性, 分数阶 Cohen-Grossberg 神经网络, 时变时延, 状态依赖切换

Abstract:

This paper primarily investigates the coexistence and stability of multiple equilibrium points for fractional-order Cohen-Grossberg neural networks (SFCGNNs) with time-varying delays and state-dependent switching. By employing the state space partition method, the existence of $5^n$ equilibrium points for SFCGNNs is established. To demonstrate the asymptotic stability of $3^n$ equilibrium points among them, the Lyapunov method is adopted. Additionally, sufficient conditions are derived to confirm the instability of the remaining equilibrium points. Finally, two numerical examples are provided to validate the effectiveness of the proposed results.

Key words: multistability, fractional-order Cohen-Grossberg neural networks, time-varying delays, state-dependent switching

中图分类号:

O175

董红勋, 万里光, 吴爱龙. 具有时变时延与状态依赖切换的分数阶 Cohen-Grossberg 神经网络的多稳定性[J]. 数学物理学报, 2026, 46(6): 2418-2432.

Hongxun Dong, Liguang Wan, Ailong Wu. Multistability of Fractional-Order Cohen-Grossberg Neural Networks with Time-Varying Delays and State-Dependent Switching[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2418-2432.

图/表 5

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