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带有延迟的分数微分方程的稳定性分析.
Divya D Joshi1, Sachin Bhalekar2, Prashant M Gade1
1Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440033, India.
本研究分析了带有时间延迟的分数微分方程的稳定性条件,这对于模拟各种系统中的长期记忆至关重要. 这些发现扩展到非线性系统,为复杂的延迟动态提供了一个框架.
科学领域:
- 动态系统和控制理论.
- 数学建模的数学建模
- 计算神经科学是一种神经科学.
背景情况:
- 长期记忆是各种系统的关键特征,通常是使用时间延迟来建模的.
- 分数顺序差异引入非局部行为,有助于长期记忆效应.
- 带延迟的分数微分方程适用于模拟表现内存的系统,但它们的稳定性分析尚未得到充分研究.
研究的目的:
- 导出和分析带有任意和分布式时间延迟的线性微分差方程的稳定性条件.
- 将稳定性分析扩展到非线性分数差异系统.
- 为理解带有内存的分数顺序系统的动态提供一个基础框架.
主要方法:
- 用任意延迟 (τ) 的线性分数微分方程来导出稳定性条件.
- 对有分布式延迟的系统进行分析.
- 具体单次延迟病例 (τ=1, τ=2) 的详细稳定性分析.
- 推导条件扩展到非线性分数差异图.
主要成果:
- 对于带有任意和分布式延迟的微分差方程,已建立稳定性条件.
- 为单次延迟t=1和t=2.2提供了详细的稳定性分析.
- 证明了衍生形式主义对非线性系统的适用性.
- 展示了框架对多次时间延迟的可扩展性.
结论:
- 该研究为具有延迟的分数微分方程提供了关键的稳定性标准,增强了复杂系统中内存的建模.
- 开发的方法适用于具有各种延迟配置的线性和非线性分数顺序系统.
- 这项工作为进一步研究具有内存的分数系统的稳定性和动态奠定了基础.
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