Breathing chimera states from purely triadic interactions

Chimera states, characterized by the coexistence of synchronized and desynchronized dynamics in identical oscillators, are typically studied in systems with pairwise interactions. Recent studies have shown that purely higher-order interactions can support chimera states. Here, we show that breathing chimera states arise in a model governed solely by a triadic phase interaction, whose intrinsic π -symmetry permits bimodal phase distributions. We construct a bimodal Ott–Antonsen reduction that incorporates an asymmetry parameter via prescribed asymmetric initial conditions, thereby achieving an exact low-dimensional description of the macroscopic dynamics. This allows us to derive an analytic condition for the emergence of chimera states and identify a bifurcation to a breathing chimera regime characterized by persistent oscillations. Furthermore, the reduced dynamics can be expressed as a Riccati-type equation, providing a geometric interpretation of the chimera state as a closed periodic orbit in the complex plane. Our results establish purely triadic coupling as a minimal higher-order mechanism for chimera formation and provide a tractable framework for studying symmetry-broken collective dynamics in systems dominated by many-body interactions.