一个混乱的地图,具有二维偏移增强
Zhihao Wang1, Chunbiao Li1, Yongxin Li1
1School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China.
Chaos (Woodbury, N.Y.)
|June 12, 2024
概括
这项研究引入了一个具有二维偏移增强的新奇混乱地图,展示了可控制的振幅和混合控制. 混乱地图显示了粒子群优化应用程序的性能和稳定性的提高.
科学领域:
- 非线性动力学是一种非线性动力学.
- 混沌理论 混沌理论
- 计算智能是一种计算智能.
背景情况:
- 洛齐地图是一个基本的混乱系统.
- 控制混乱系统振幅对于应用至关重要.
- 在混乱系统中的多稳定性提供了多样化的动态行为.
研究的目的:
- 详尽研究一个混乱的地图与二维偏移增强.
- 揭示偏移增速的机制及其对动态的影响.
- 在优化中探索混合控制策略和应用.
主要方法:
- 来自洛齐地图的衍生.
- 通过反期取消对抵消提升机制的分析.
- 在不同的初始条件下研究多稳定性.
- 使用微控制器进行数值模拟和电路实现.
主要成果:
- 通过偏移增强来证明振幅的可控性.
- 揭示了同质和异质多稳定性的共存.
- 在不改变Lyapunov指数的情况下识别了振幅重新缩放的独立常量项.
- 通过绑定振幅控制和偏移增强参数引入混合控制.
- 通过电路实现和数值模拟验证了理论发现.
结论:
- 新的混乱地图提供精确的振幅控制,并表现出丰富的多稳定性.
- 混合控制为管理混乱动态提供了一种独特的方法.
- 混乱的地图显示出优越的性能和强度,用于粒子群集的优化.
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