Persistence of bistability across the full η range for two-population cluster/alternating chimera states

Ascertain whether bistability between two-population cluster states (alternating chimera) and nearly in-phase locked states persists across the entire range of the homeostasis parameter η in the adaptive Kuramoto oscillator network with a two-population subgraph constraint that enforces decay of inter-population edges at rate η^{-1}.

Background

For intermediate values of η under the two-population subgraph constraint, the authors observe rich dynamics including two-population clusters that alternate roles (alternating chimera) and adaptive chimera states where one cluster is coherent while the other exhibits periodic oscillations in its order parameter.

They report bistability between such states and nearly in-phase locked configurations over a range of η, and explicitly state that it remains open whether this bistability persists across the entire η domain, motivating a systematic investigation of parameter dependence and persistence.