У оквиру семинара Центра за изучавање комплексних система Института за физику у Београду, у четвртак, 28. августа 2025. године у 14 часова у сали „Звонко Марић“ Института за физику, др Ива Бачић (Истраживачки центар Јилих) одржаће предавање:
Phase locking and multistability in the topological Kuramoto model on cell complexes
САЖЕТАК:
The topological Kuramoto model generalizes classical synchronization theory to higher-order interactions, with oscillator dynamics defined on cells of arbitrary dimension within simplicial or cell complexes. While
previous work has largely focused on simplicial complexes, many natural and engineered systems are better described by cell complexes. Wedevelop an algorithm that identifies all phase-locked states of the
topological Kuramoto model on arbitrary cell complexes. By applying this framework to rings, Platonic solids, and simplexes, as minimal representative motifs of larger networks, we derive explicit winding-number bounds that determine the number of coexisting stable states. We also demonstrate structural cascades of multistability, inherited from both lower and higher dimensions. Cell complexes can support richer multistability than simplicial complexes of the same dimension. Moreover, we show that multistability patterns are organized into universality classes, grouping distinct complexes that share certain structural features. Our framework can be extended to arbitrary cell complexes, as well as arbitrary higher-order oscillator networks. Applications include power-grid stability, optical and mechanical oscillator arrays, and neural ensembles, among others.