发表机构
Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University; Bharathidasan University; SRM TRP Engineering College; Easwari Engineering College（尼赫鲁纪念学院（自治），隶属于巴拉蒂达桑大学; 巴拉蒂达桑大学; SRM TRP工程学院; 伊斯瓦里工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过耦合多个一维阻尼受迫Higgs振荡器，揭示共形质量以幂律关系调节速度极值从而引发极端事件，并量化能量同步误差以阐明其机制。
AI 中文摘要
定义在弯曲空间上的振荡器为探索几何诱导的非线性动力学提供了一个自然框架。二维Mathews-Lakshmanan振荡器和Higgs振荡器是几何诱导非线性振荡器的突出例子。平坦空间中的二维Higgs振荡器源于球面S2上的谐振子通过共形（球极）投影到二维平面。其一维对应物由具有曲率参数的非欧几里得几何定义，在受到阻尼和外部驱动力时表现出混沌动力学和极端事件（EEs）[1]。在本工作中，我们通过多个一维阻尼和受迫Higgs振荡器之间的质量相互作用引入耦合，并在多粒子框架内研究由此产生的集体非线性动力学。更重要的是，我们通过幂律关系建立了共形质量m(x)与速度极值之间的联系，展示了共形质量如何调节导致极端事件（EEs）出现的转向点。此外，为了对潜在机制提供额外见解，我们量化了振荡器之间的能量同步误差，从而揭示了在EEs发生期间能量同步如何演变。
英文摘要
Oscillators defined on curved spaces provide a natural framework for exploring geometry-induced nonlinear dynamics. The two-dimensional Mathews-Lakshmanan oscillator and Higgs oscillator are prominent examples of geometrically induced nonlinear oscillators. The two-dimensional Higgs oscillator in flat space arises from a conformal (stereographic) projection of the harmonic oscillator on the sphere S2 onto the two-dimensional plane. Its one-dimensional counterpart, defined by a non-Euclidean geometry with curvature parameter, exhibits chaotic dynamics and extreme events (EEs) when subjected to damping and external driving forces [1]. In this work, we introduce coupling through mass interaction among multiple one-dimensional damped and forced Higgs oscillators and investigate the resulting collective nonlinear dynamics within a many-particle framework. More importantly, we establish the connection between the conformal mass m(x) and the extrema of velocity through a power-law relation, demonstrating how the conformal mass regulates the turning points leading to the emergence of extreme events (EEs). Furthermore, to provide additional insight into the underlying mechanism, we quantify the energy synchronization error among the oscillators, thereby revealing how energy synchronization evolves during the onset of EEs.
CommentsAccepted for Publication in Physical Review E
