等分网络粗粒化条件下嵌合体态的条件保持

中文摘要 AI 辅助

嵌合体态以耦合振子网络中相干与不相干动力学共存为特征，是非线性系统中最引人入胜的集体现象之一，并深受底层拓扑结构和初始条件的影响。在大规模网络中对嵌合体态进行分析仍具有很高的计算需求，这促使人们发展粗粒化策略，即在缩减网络规模的同时保留嵌合体行为的基本动力学特征。在本快报中，我们研究了基于等分的商图能否在网络规模大幅缩减的情况下保持嵌合体模式。利用非局域耦合的FitzHugh-Nagumo（FHN）振子，我们利用了这样一个事实：对于等分划分，限制在相应簇同步子空间上的全网络动力学与商动力学完全一致。我们探究这种结构上的精确性是否足以在网络规模缩减后保持嵌合体特征。我们的结果表明，情况并非必然如此：商动力学与全网络嵌合体动力学之间的一致性取决于等分划分，且精确的商动力学并不一定保证相应全网络轨迹的横向稳定性。重要的是，当簇同步解变得横向不稳定时，全网络可能偏离精确的商轨迹，但仍保持在宏观嵌合体状态。因此，结构精确性与动力学保持是不同的要求，横向稳定性为评估基于商的嵌合体态粗粒化提供了补充判据。

英文摘要

Chimera states, characterized by the coexistence of coherent and incoherent dynamics in networks of coupled oscillators, are among the most intriguing collective phenomena in nonlinear systems and are strongly shaped by the underlying topology and initial conditions. Their analysis in large-scale networks remains computationally demanding and motivates the development of coarse-graining strategies that reduce network size while retaining the essential dynamical features of chimera behavior. In this Letter, we investigate whether equitable-partition-based quotient graphs can preserve chimera patterns under substantial reductions of network size. Using nonlocally coupled FitzHugh-Nagumo (FHN) oscillators, we exploit the fact that, for an equitable partition, the full-network dynamics restricted to the associated cluster-synchronous subspace coincide exactly with the quotient dynamics. We ask whether this structural exactness is sufficient to preserve chimera signatures after the network size reduction. Our results show that this is not necessarily the case: agreement between quotient and full-network chimera dynamics depends on the equitable partition, and exact quotient dynamics do not necessarily guarantee the transverse stability of the corresponding full-network trajectory. Importantly, when the cluster-synchronous solution becomes transversely unstable, the full network may depart from the exact quotient trajectory while remaining in a macroscopic chimera regime. Therefore, structural exactness and dynamical preservation are distinct requirements, and transverse stability provides a complementary criterion for assessing quotient-based coarse-graining of chimera states.

发表机构

• IMT School for Advanced Studies（IMT高等研究院）

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