XPPLORE: Import, visualize, and analyze XPPAUT data in MATLAB

The paper demonstrates, by software and code examples, how to (i) reconstruct a manifold of limit cycles from XPPAUT ‘.auto’ outputs via column-wise concatenation of periodic-orbit samples with equal sampling length (Func_Manifold) and (ii) compute the averaged slow drift ⟨ċ⟩ using normalized-by-period time and trapz, selecting the orbit where |⟨ċ⟩| is minimal; however, it does not supply formal assumptions or proofs of continuity, surface convergence, or existence of a true zero crossing for J(c) (it explicitly implements a numerical minimum rather than a root-finding argument) . The candidate solution provides the missing mathematics: a precise parametrization Φ of the limit-cycle surface, uniform convergence of bilinear interpolants implying Hausdorff convergence of the reconstructed surfaces, continuity of J(c), and an IVT-based existence of c* under a sign change, plus a consistent numerical scheme. These steps are logically sound given the stated hypotheses (continuity, single branch, phase alignment).