对于一般化系统的强烈扰动的键轨道吸引器
A Dlamini1, E F Doungmo Goufo1, M Khumalo1
1Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa.
Chaos (Woodbury, N.Y.)
|February 3, 2025
概括
这项研究探讨了带有带轨吸引子的混乱系统,检查了古典和分数顺序模型. 微积分运算,使用卡普托-法布里齐奥运算子,揭示了复杂的动态和内存效应,通过硬件实现验证.
科学领域:
- 非线性动力学和混沌理论
- 分数微积分的计算.
- 应用数学 应用数学 应用数学
背景情况:
- 混乱系统表现出复杂的动态,通常通过吸引器可视化.
- 一般化的微分方程可以建模复杂的系统.
- 分数计算为分析具有记忆效应的系统提供了先进的工具.
研究的目的:
- 为了分析带有带轨吸引器的一般化混乱系统.
- 调查该系统的经典版本和分数顺序版本.
- 通过分析,数值和硬件实现来验证发现.
主要方法:
- 分析和数值检查经典和分数顺序的混乱系统.
- 收和稳定性的分析.
- 基于现场可编程门阵列 (FPGA) 的电路实现,用于硬件验证.
主要成果:
- 在经典的混乱系统中证实了键轨道吸引器的存在.
- 在使用卡普托-法布里齐奥运算子的分数顺序系统中出现键轨道吸引器.
- 观察到分数顺序吸引器中的扰动和一致的硬件验证结果.
结论:
- 分数计算,特别是卡普托-法布里齐奥运算子,有效地捕捉了混乱动态中的记忆效应.
- 该研究将混乱系统的理论建模与实际硬件应用相结合.
- 结果为各种科学领域的复杂系统建模提供了宝贵的见解.
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