Parameter identification from single trajectory data: from linear to nonlinear

The paper establishes, largely via computation plus concise arguments, (i) trivial non-uniqueness on periodic LV orbits using time-rescaling, (ii) the presence of fold curves Cf1,Cf2 where the solution count changes by two and, in particular, a vertical cross-section at fixed x2>x1^2/x0 with a fold at yF<y0 producing two solutions with σA=[−+−+], and (iii) that a rotated-field perturbation removes this fold for sufficiently large positive p and deepens it for negative p; it also documents multiple coexisting solutions in the saturated LV model at ε=1. These claims are explicitly stated and/or illustrated in the paper (trivial rescaling argument in Section 4.1; fold cross-sections and Cf1,Cf2 in Figure 7/Section 4.2.4; rotated-field and saturation effects in Section 5) . The model (candidate solution) reaches the same substantive conclusions, but gives a more formal framing using the implicit function theorem and generic singularity (fold/cusp) theory and a Hamiltonian calculation for the rotated field. Thus, both are correct; the paper’s case is empirical/theoretical, while the model’s case supplies a complementary, more structural proof sketch.