Symmetry-breaking death states and bistability in chiral oscillator networks with higher-order interactions
摘要
We explore the impact of higher-order interactions in a chiral oscillator network composed of identical limit-cycle oscillators coupled through both pairwise and triplet (three-body) interactions. The network contains an equal number of clockwise- and counterclockwise rotating oscillators, resulting in a symmetric distribution of opposing frequencies. This symmetry gives rise to rich collective dynamics, including mixed states such as symmetric – antisymmetric death (SAD) and antisymmetric–symmetric death (ASD). Using a reduced model, we derive analytical stability conditions and map the existence of these states in the space of pairwise and higher-order coupling strengths. Bifurcation analysis reveals transitions between oscillatory and death states, while basin of attraction analysis confirms bistable regimes involving the coexistence of mixed synchronization and ASD, and of SAD and ASD. These findings are validated in larger networks, showing excellent agreement with predictions from the reduced model and revealing complex collective transitions. Finally, breaking frequency symmetry by introducing an asymmetric distribution of counter-rotating oscillators induces a transition from symmetric-breaking oscillation-death states to symmetry-breaking cluster oscillatory states as the higher-order coupling increases. We believe that these results demonstrate the essential role of higher-order interactions in shaping chirality-driven symmetry-breaking dynamics and uncover mechanisms that govern rhythmic behavior in biological and engineered oscillator networks.