时变高阶结构上的全局同步
Global synchronization on time-varying higher-order structures
AI总结：
本文研究时变高阶结构对全局同步的影响，通过扩展主稳定性形式体系，纳入高阶结构时间演化带来的额外贡献，并在Stuart-Landau振荡器和Lorenz混沌振荡器上验证了理论的有效性。
摘要：
同步现象在静态网络或高阶结构（如超图和单纯复形）上演化的系统中受到了科学界的广泛关注。在许多相关的实际应用中，这些高阶结构并非静态，而是随时间演化的，因此本文讨论了高阶结构的时变特性对全局同步涌现的影响。为实现这一目标，我们扩展了主稳定性形式体系，以一般性方式计入支撑动力系统的高阶结构随时间演化所产生的额外贡献。该理论通过两个示例进行了成功验证，即Stuart-Landau非线性振荡器和Lorenz混沌振荡器。
英文摘要：
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the latter are not static but do evolve in time, in this paper we thus discuss the impact of the time-varying nature of high-order structures in the emergence of global synchronization. To achieve this goal we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart-Landau nonlinear oscillator and the Lorenz chaotic oscillator.
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