Chaotic switching in driven-dissipative Bose-Hubbard dimers: when a flip bifurcation meets a T-point in R4

The paper establishes the local structure on Fix(η) analytically (cubic (6), cusp CP) and presents extensive numerical evidence for the global picture (Bykov T-point with a robust q→p connection in Fix(η), wedge bounded by EtoP curves and families of Shilnikov curves, heteroclinic fold F and the degenerate singular cycles at CF, and a Z2-equivariant flip point Fl on HOMq) . The candidate solution matches the phenomenon-by-phenomenon storyline and cites standard theory to argue genericity, but it does not verify key hypotheses (e.g., precise eigenvalue configurations and manifold orientations, unimodality of the return map, inclination-flip conditions), making it a plausibility argument rather than a complete proof. The paper, in turn, clearly signals reliance on numerics for several codimension-two features (especially Fl) rather than a full proof. Hence, both are aligned but incomplete in rigor.