GENERALIZED PITCHFORK BIFURCATIONS IN D-CONCAVE NONAUTONOMOUS SCALAR ORDINARY DIFFERENTIAL EQUATIONS

The paper’s Theorem 3.1 rigorously establishes the three-way bifurcation trichotomy for x' = f(ω·t,x) + λx under (Co) and (SDC)*, including precise hyperbolicity of M0 determined by the Sacker–Sell spectrum and residual collisions at λ+. The candidate model reproduces the same classification and spectral conclusions and correctly identifies the attractor’s delimiter structure and ordering. Its proof route is different (spectral-shift plus a concavity-driven contraction argument) and broadly sound, though some steps (e.g., the residual-collision proof and ‘no fourth minimal set’ exclusion) are sketched and rely on unstated lemmas. Hence, both arrive at the same conclusions; the paper provides a complete rigorous treatment, while the model offers a compatible but less formal proof sketch.