几乎肯定指数趋同分析时间延迟不确定的细胞神经网络 通过Liu过程驱动Liu过程通过Lyapunov-Krasovskii功能方法
Chengqiang Wang1, Zhifu Jia1, Yulin Zhang2
1School of Mathematics, Suqian University, Suqian 223800, China.
Entropy (Basel, Switzerland)
|November 24, 2023
概括
这项研究证明,由过程驱动的时间延迟不确定的细胞神经网络具有独特的平衡状态. 建立了收标准,证明了这些状态的几乎肯定指数稳定性.
科学领域:
- 动态系统和控制理论.
- 计算神经科学是一种神经科学.
- 随机过程 随机过程
背景情况:
- 不确定性理论模型不确定性,类似于概率理论.
- 时间延迟的不确定细胞神经网络 (UCNN) 在复杂系统中越来越多地使用.
- 分析UCNN的稳定性和趋同性对于其应用至关重要.
研究的目的:
- 研究由过程驱动的时间延迟UCNN中的状态轨迹的收性质.
- 建立这些网络中平衡状态的存在和独特性条件.
- 制定UCNNs几乎确定的指数稳定性的标准.
主要方法:
- 应用经典的巴纳克定点定理来证明独特的平衡状态的存在.
- 一个新的Lyapunov-Krasovskii函数的设计,以导出收标准.
- 使用随机分析来证明几乎确定的指数稳定性.
主要成果:
- 在特定条件下的时间延迟UCNN的独特平衡状态的证明.
- 基于设计的利亚普诺夫-克拉索夫斯基函数的趋同标准的开发.
- 证明平衡状态几乎肯定是指数稳定的,轨迹指数趋同.
结论:
- 该研究提供了一个严格的数学框架,用于分析由不确定的过程驱动的UCNN的稳定性.
- 开发的标准通过使用一般的正确确矩阵来减少保守主义.
- 这项研究为研究不确定的神经网络提供了新的见解和方向.
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