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. Whether higher-order interactions alone can generate such symmetry-broken collective states remains unclear. Here, we show that chimera states can arise solely from triadic interactions. Furthermore, exploiting the intrinsic $\pi$-symmetry of the triadic coupling leads to bimodal phase distributions. We construct a bimodal Ott--Antonsen reduction that incorporates an asymmetry parameter via symmetry-breaking 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 mechanism for chimera formation and provide a tractable framework for studying symmetry-broken collective dynamics in systems dominated by many-body interactions.