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分数级反应-扩散惯性时间延迟神经网络的稳定性和同步性,具有参数扰动
Hu Wang1, Yajuan Gu2, Xiaoli Zhang3
1School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China.
本研究分析了带有时间延迟的分数级通用反应扩散惯性神经网络 (FGRDINNs). 它使用利亚普诺夫方法建立了全球统一的稳定性和同步条件,并通过数值模拟验证.
科学领域:
- 计算神经科学是一种神经科学.
- 非线性动力学是一种非线性动力学.
- 控制理论 控制理论
背景情况:
- 分数顺序系统比整数顺序系统提供了增强的建模功能.
- 反应-扩散惯性神经网络 (FGRDINNs) 是复杂的动态系统,在各种领域都有应用.
- 时间延迟在分析神经网络的稳定性和同步性方面带来了重大挑战.
研究的目的:
- 为了研究分数顺序的一般化反应-扩散惯性神经网络 (FGRDINNs) 与时间延迟的全球均稳定性.
- 根据不同的控制策略和参数扰动,得出FGRDINNs与时间延迟的全球同步条件.
- 通过数值模拟验证理论发现,并分析控制器参数的影响.
主要方法:
- 使用利亚普诺夫比较原理来分析FGRDINNs的全球均稳定性.
- 使用利亚普诺夫直接方法来建立全球同步标准.
- 提供了数值示例,以证明推导理论结果的有效性.
主要成果:
- 该研究提供了严格的数学条件,以确保FGRDINNs与时间延迟的全球统一稳定性.
- 全球同步条件得出,考虑反控制和参数变化的影响.
- 数字模拟证实了理论预测,并说明了FGRDINNs的行为.
结论:
- 这项研究成功地建立了复杂的FGRDINNs与时间延迟的稳定性和同步性的理论框架.
- 这些发现有助于更深入地了解分数级神经网络的动态,并为控制设计提供实用见解.
- 该研究强调了基于Lyapunov的方法在分析先进的神经网络模型中的重要性.
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