论文标题
简单振荡器种群的分叉分析和结构稳定性
Bifurcation analysis and structural stability of simplicial oscillator populations
论文作者
论文摘要
我们为振荡器合奏的集体动力学提供了一个分析描述，该振荡器合奏用简单结构编码的高阶耦合，这是用于脑功能和信息存储的说明性和有见地的范式。系统的新型动力学（包括突然的对同步和多稳定性）是严格的特征，并且发现与一阶相变连续的临界点相对应满足通用缩放属性。更重要的是，使用稳定群集状态的严格光谱分析来表征具有任意集成大小的多个群集的潜在分叉机制。由于$ so_2 $组对称性，我们表明，突然的对异步转变的连续体是由于在高维相空间中非平凡的反对称歧管下的集体模式的不稳定性而产生的。
We present an analytical description for the collective dynamics of oscillator ensembles with higher-order coupling encoded by simplicial structure, which serves as an illustrative and insightful paradigm for brain function and information storage. The novel dynamics of the system, including abrupt desynchronization and multistability, are rigorously characterized and the critical points that correspond to a continuum of first-order phase transitions are found to satisfy universal scaling properties. More importantly, the underlying bifurcation mechanism giving rise to multiple clusters with arbitrary ensemble size is characterized using a rigorous spectral analysis of the stable cluster states. As a consequence of $SO_2$ group symmetry, we show that the continuum of abrupt desynchronization transitions result from the instability of a collective mode under the nontrivial antisymmetric manifold in the high dimensional phase space.
