Mechanism underlying metastable chimera states in hierarchically modular oscillator networks

Determine the precise mechanism that leads to metastable chimera states in the second and third hierarchical layers of three-layer hierarchically modular networks of identical Kuramoto-Sakaguchi oscillators with phase lags, particularly at the transition where stable and breathing chimera states cease to exist.

Background

The paper demonstrates that hierarchically modular networks of identical Kuramoto-Sakaguchi oscillators can exhibit stable, breathing, and metastable chimera states depending on the mesoscale structural parameter H. Using Laplacian renormalization group flow, the authors relate stable and breathing chimera states to slow eigenmodes but note that metastable chimera states arise in a parameter regime where the two-population model analogy no longer suffices.

Because the time-rescaled system loses fine-grained information and the observed parameter regime departs from classical analytical results, the authors suggest that an analytical approach is needed to pin down the mechanism driving metastable chimera states, and acknowledge possible finite-size effects.