Department of Electrical, Electronics and Computer Science Engineering, University of Catania, Catania, Italy.
CNR-Institute of Complex Systems, Florence, Italy.
Nat Commun. 2021 Feb 23;12(1):1255. doi: 10.1038/s41467-021-21486-9.
Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.
物理学、生物学、社会科学和工程学中的各种系统已经成功地建模为耦合动力系统网络，其中的链接描述了两两相互作用。然而，这是一个过于严格的限制，因为最近的研究表明，高阶多体相互作用存在于社会群体、生态系统和人类大脑中，并且它们实际上会影响所有这些系统的涌现动力学。在这里，我们引入了一个通用框架来研究耦合动力系统，该框架考虑了其相互作用的任何可能阶次的精确微观结构。我们表明，完全同步是作为一个不变解存在的，并给出了将其作为稳定状态观察到的必要条件。此外，在某些相关情况下，这样的必要条件采用主稳定性函数的形式。这将对两两相互作用有效的现有结果推广到具有最一般可能结构的复杂系统的情况。
