分析一类双延迟分数微分方程
Sachin Bhalekar1, Pragati Dutta1
1School of Mathematics and Statistics, University of Hyderabad, Hyderabad 500046, India.
Chaos (Woodbury, N.Y.)
|January 27, 2025
概括
本研究分析了两个延迟的分数延迟微分方程中的稳定性. 它确定了不同的稳定区域,包括单个稳定区域 (SSR) 和稳定切换 (SS) 区域,对于建模复杂系统至关重要.
科学领域:
- 数学 数学 是一个数学.
- 动态系统 动态系统
- 控制理论 控制理论
背景情况:
- 分数顺序延迟微分方程模型复杂系统具有内存效应.
- 具有多个延迟的方程对于模拟具有多个交互过程的系统至关重要.
- 了解稳定性对于预测系统行为和确保可靠运行至关重要.
研究的目的:
- 执行一个分数顺序延迟微分方程与两个离散延迟的全面稳定性和分叉分析.
- 为了研究系统参数对ab平面稳定性的影响.
- 识别和描述不同的稳定区域,包括稳定,不稳定,单个稳定区域 (SSR) 和稳定开关 (SS).
主要方法:
- 分数顺序延迟微分方程Dαx(t) =ax(t) +bx(t-τ) -bx(t-2τ) 的分析.
- 在参数空间 (ab-plane) 中确定稳定性标准.
- 确定导致分叉的关键延迟值.
主要成果:
- 该研究划分了不同的稳定区域:稳定,不稳定,单个稳定区域 (SSR) 和稳定开关 (SS).
- 在稳定的区域中,系统对所有延迟值保持稳定.
- 在SSR区域出现稳定性转换时,SSR区域表现出关键延迟值,而SS区域则表现出切换行为.
结论:
- 分析提供了一个详细的稳定性地图,分数延迟微分方程的两个延迟.
- 确定的稳定区域 (SSR,SS) 对于理解和控制这些系统的动态至关重要.
- 这项工作为建模和分析具有多次时间延迟的复杂动态系统的理论框架做出了贡献.
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