Coexistence of multistable synchronous states in a three-oscillator system with higher-order interaction

Abstract

We study a three-oscillator system with pairwise (1-simplex) and triadic (2-simplex) interactions, and focus on how the interplay between these two types of interactions influences synchronous dynamics. Using a minimal model, dynamical phenomena in systems that have been previously studied under the thermodynamic limit ($N\to \infty$) are further clarified. Various synchronous states, including in-phase and antiphase synchronous states, as well as partial synchronous states are demonstrated. Meanwhile, significant multistable behaviors are revealed. Our work extends previous research on pairwise and triadic interactions, which can deepen our understanding of the impact of correlation between higher-order interaction and multistability. These dynamic phenomena bear resemblance to the diverse synchronization patterns of the heart, and they also serve as pivotal factors in information storage and memory retention within the brain.