标题： 全局耦合高阶网络上的自组织双稳态 显示英文标题

标题： Self-organized bistability on globally coupled higher-order networks

摘要： 自组织双稳态（SOB）是系统在微妙调整自身至双稳态边缘时表现出的关键行为，其特征是具有第一阶相变。 其本质在于系统能够通过控制参数的自我调节，在共存状态之间经历持久的转换。 最近，SOB已被确立为一种无标度网络中反复过渡到全局同步的短暂状态。 在此，我们进行一项理论探索，将SOB概念的边界扩展到高阶网络（隐式地微观嵌入在单纯复形中），同时考虑耦合约束所施加的限制。 通过在热力学极限下对高阶网络应用Ott-Antonsen维数约简，我们推导出在耦合限制下的SOB条件，这些条件与有限尺寸系统的数值模拟结果高度一致。 我们使用连续同步图和自发同步事件的统计数据，来证明SOB在启动和终止临时同步事件中的关键作用。 我们表明，在弱耦合消耗下，这些自发现象非常类似于癫痫大脑功能的统计特征。 显示英文摘要

摘要： Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.