Breathing chimera states from purely triadic interactions
arXiv:2607.28017
The paper shows that chimera states—coexisting synchronized and desynchronized groups—can emerge solely from triadic (three-way) interactions among identical oscillators, and derives an exact low-dimensional description via a bimodal Ott‑Antonsen reduction that predicts a breathing chimera regime.
Abstract
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 -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.
17 pages, 5 figures, and 1 ancillary video (main text: 10 pages, 3 figures; Supplemental Material: 7 pages, 2 figures). Submitted to Chaos, Solitons & Fractals