Abstract
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.
Highlights
Spontaneous synchronization in populations of interacting units is a ubiquitous phenomena in complex systems [1,2]
Most existing literature focuses on pairwise interaction between oscillators that typically contain the first harmonic based on a phase reduction [9,10]
As shown in Refs. [18,19,20], notable features of higher-order interactions in coupled oscillator ensembles include the emergence of extensive multistability and a continuum of abrupt desynchronization transitions (ADTs), which lead to potential applications in memory and information storage
Summary
Spontaneous synchronization in populations of interacting units is a ubiquitous phenomena in complex systems [1,2] Describing such collective behaviors in terms of coupled phase oscillators and studying phase transitions between incoherence and synchrony have proven useful in of physics, biology, and social systems [3,4,5]. [18,19,20], notable features of higher-order interactions in coupled oscillator ensembles include the emergence of extensive multistability and a continuum of abrupt desynchronization transitions (ADTs), which lead to potential applications in memory and information storage. Despite these findings, a rigorous analysis of the bifurcations and stability properties that characterize both the.
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