发表机构
Tohoku University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示线性增长率异质性与复全局耦合可在相同频率的Stuart-Landau振子群体中产生准周期与混沌，并通过Lyapunov谱、不变流形及系综采样阐明其分岔与多稳态机制。
AI 中文摘要
我们证明，线性增长率异质性与复全局耦合相结合，可以在具有相同自然频率且无Kerr型非线性频移的有限Stuart-Landau振子群体中产生准周期性和混沌。Lyapunov谱识别出极限环、准周期环面和混沌吸引子，而序参量振幅表现出与通向混沌的倍周期分岔类转变一致的迹象。我们进一步推导了一个有限大小的不变流形，由边长固定的闭合多边形表示的零序参量锁相解组成，并展示了其依赖于构型的横向稳定性。系综采样揭示了多边形和普通锁相周期、准周期环面以及混沌吸引子之间显著的共存现象。振幅-时间重标度识别出大致组织相界以及相似分岔和多稳态模式的主要参数。这些结果通过揭示异质性和复耦合如何共同塑造动力学复杂性、分岔结构和多稳态，增进了我们对包含振幅的振子网络中集体动力学的理解。
英文摘要
We show that linear-growth-rate heterogeneity combined with complex global coupling can generate quasiperiodicity and chaos in a finite population of Stuart-Landau oscillators with identical natural frequencies and no Kerr-type nonlinear frequency shift. Lyapunov spectra identify limit cycles, quasiperiodic tori, and chaotic attractors, while the order-parameter amplitude exhibits signatures consistent with period-doubling-like transitions towards chaos. We further derive a finite-size invariant manifold of vanishing-order-parameter phase-locked solutions represented by closed polygons with fixed side lengths and demonstrate their configuration-dependent transverse stability. Ensemble sampling reveals pronounced coexistence among polygonal and ordinary phase-locked cycles, quasiperiodic tori, and chaotic attractors. An amplitude-time rescaling identifies the leading parameter approximately organizing the regime boundaries and the similar bifurcation and multistability patterns. These results advance our understanding of collective dynamics in amplitude-inclusive oscillator networks by revealing how heterogeneity and complex coupling jointly shape dynamical complexity, bifurcation structure, and multistability.
Comments33 pages, 8 figures
