对于具有离散和分布式延迟的分数级BAM神经网络,新的延迟依赖的统一稳定性标准
1Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Chengalpattu, Tamil Nadu, India.
Network (Bristol, England)
|March 26, 2025
概括
这项研究引入了带有记忆的分数级神经网络,将稳定性条件扩展到两个变量. 该研究使用线性矩阵不等式建立了依赖延迟的稳定性标准,通过数值示例验证.
科学领域:
- 神经网络的神经网络的神经网络
- 分数微积分的计算.
- 控制理论 控制理论
背景情况:
- 分数顺序系统比传统的整数顺序系统提供了增强的建模功能.
- 双向关联记忆 (BAM) 神经网络对于关联记忆任务至关重要.
- 分数顺序系统的稳定性分析,特别是在延迟的情况下,会带来独特的挑战.
研究的目的:
- 在两个变量中开发一类卡普托分数顺序双向联想记忆神经网络.
- 将拉祖米金型的统一稳定条件扩展到这些复杂的系统中.
- 为实际应用推导取决于延迟的统一稳定性标准.
主要方法:
- 开发一个新的卡普托分数顺序BAM神经网络模型.
- 对单变量系统的拉祖米金型稳定性标准扩展到两个变量延迟分数系统.
- 用利亚普诺夫函数和线性矩阵不等式 (LMI) 进行稳定性分析.
主要成果:
- 成功地将拉祖米金型的统一稳定条件扩展到两个变量延迟的卡普托分数系统.
- 由延迟依赖的统一稳定性标准衍生,用LMI表示.
- 通过两个数值示例证明了理论发现的有效性和实用性.
结论:
- 拟议的方法提供了一个强大的框架来分析带有延迟的分数级BAM神经网络的稳定性.
- 基于LMI的衍生标准是计算可处理的,并且有效地评估系统稳定性.
- 数字示例证实了理论结果在现实场景中的有效性和适用性.
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