Discretized Fast–Slow Systems with Canards in Two Dimensions

Abstract We study the problem of preservation maximal canards for time discretized fast–slow systems with canard fold points. In order to ensure such preservation, certain favorable structure-preserving properties discretization scheme are required. Conventional schemes do not possess properties. perform a detailed analysis an unconventional due Kahan. The uses blow-up method deal loss normal hyperbolicity at point. show that Kahan quadratic vector fields imply similar result as in continuous time, guaranteeing occurrence between attracting and repelling slow manifolds upon variation bifurcation parameter. proof is based on Melnikov computation along invariant separating curve, which organizes dynamics map similarly ODE problem.