在适应性萨卡古奇-库拉莫托模型中,过渡到同步,具有更高阶相互作用
Sangita Dutta1, Prosenjit Kundu2, Pitambar Khanra3,4
1National Institute of Technology, Department of Mathematics, Durgapur 713209, India.
Physical review. E
|February 7, 2025
概括
我们研究了萨卡古奇-库拉莫托模型中的同步过渡与更高阶相互作用. 我们发现了连续和不连续的过渡,包括爆炸和分层同步,使用模拟和缩小模型.
科学领域:
- 复杂的系统复杂的系统.
- 非线性动力学是一种非线性动力学.
- 统计物理学的统计物理.
背景情况:
- 萨卡古奇-库拉莫托模型是研究合振荡器系统同步现象的基本框架.
- 了解过渡动态对于描述各种系统中新兴的集体行为至关重要.
研究的目的:
- 调查萨卡古奇-库拉莫托模型中与高阶相互作用和全球秩序参数适应过渡到同步的过程.
- 描述不同类型的同步过渡,包括连续和不连续的.
主要方法:
- 完整的萨卡古奇-库拉莫托系统的广泛的数值模拟.
- 使用奥特-安东森的替代模型 (Ott-Antonsen ansatz) 来推导和分析一个减少顺序模型 (ROM).
- 对同步状态的分析稳定性分析.
主要成果:
- 数字模拟显示了连续的 (第二阶段) 和不连续的过渡 (第一阶段和分层同步).
- 减少顺序模型准确地复制了模拟结果,为参数依赖的过渡场景提供了更深入的见解.
- 不同的过渡类型与特定的分叉联系在一起:第二阶段到超临界叉分叉 (PB),分层到多个结 (SN) 分叉和超临界PB,以及第一阶段到亚临界PB和SN分叉.
结论:
- 这项研究成功地将萨卡古奇-库拉莫托模型中的多种同步过渡场景与更高阶相互作用进行了表征.
- 减少顺序模型作为一种强大的分析工具,用于理解复杂的同步动态.
- 已识别的分叉机制提供了对新出现的同步模式的基本理解.
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