科恩-格罗斯伯格神经网络的周期性解决方案的全球指数稳定性
Kuo-Shou Chiu1, Jyh-Cheng Jeng2, Tongxing Li3
1Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, José Pedro Alessandri 774, Santiago, Chile.
Cognitive neurodynamics
|August 22, 2025
概括
这项研究建立了Cohen-Grossberg神经网络中周期性解决方案和全球指数稳定的条件,并通过模拟证实了整体化的断片常量延迟.
科学领域:
- 计算神经科学
- 动态系统理论
- 应用数学
背景情况:
- 科恩-格罗斯伯格神经网络是神经科学中的基本模型.
- 了解这些网络的稳定性和周期性对于其应用至关重要.
- 整体化的断片常量延迟使网络动态变得复杂.
研究的目的:
- 研究科恩-格罗斯伯格神经网络模型的全球指数稳定性.
- 建立在总体化零碎持续延误的情况下存在周期性解决方案的条件.
- 通过数值模拟验证理论发现.
主要方法:
- 施舍弗定点定理的应用以保证周期性解决方案.
- 针对整体的分数不等式的开发.
- 在特定延迟条件下分析网络动态.
主要成果:
- 确定了周期性溶液存在的充分条件.
- 为全球指数稳定提供了足够的条件.
- 计算机模拟显示了一个全球指数稳定的周期性Cohen-Grossberg神经网络.
结论:
- 这项研究为分析延迟神经网络提供了一个强大的框架.
- 这些发现证实了理论结果的可行性和有效性.
- 这项研究有助于复杂神经网络模型的稳定性分析.
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