A Novel Route to Oscillations via non-central SNICeroclinic Bifurcation: unfolding the separatrix loop between a saddle-node and a saddle

On the core constructions (local/global maps, codimension-three identification, and the equations of the homoclinic and SNIC curves), the paper and candidate largely agree. The paper develops T12 and T34 explicitly, fixes a1 = a2 = −1, and derives the homoclinic p2 → p2 locus μ2 = −a1 T12(μ3) with μ3 > 0 and the non-central SNIC pq1 → pq1 locus μ3 = −a2 T34(μ2) with μ2 < 0, and analyzes the μ1 ≶ 0 cases consistently with those maps . However, the model’s quadrant-wise summary contradicts the paper: the paper states that in the second quadrant (μ2 < 0, μ3 > 0) both separatrices tend to the periodic orbit, whereas the model claims no small periodic orbit exists in QII; likewise, the paper specifies thresholds within QI and QIII where periodic orbits persist or are destroyed, while the model’s statement oversimplifies these regions . For μ1 > 0, the paper’s statements μ3 = −a2 T34(μ2) + √μ1 for a p1-homoclinic and μ2 = −a1 T12(μ3) with μ3 > √μ1 for a p2-homoclinic agree with the model’s formulas, but the model’s quadrant-level claim remains at odds with the paper’s detailed region descriptions . Given this material discrepancy in the parameter-plane classification, the paper’s account is correct on that point and the model is not.