2008/12/11 by Thomas Forget, Forget, Thomas
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0812.2226
openalex publication_date 2008/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with the asymptotic study of the so-called canard solutions, which arise in the study of real singularly perturbed ODEs. Starting near an attracting branch of the "slow curve", those solutions are crossing a turning point before following for a while a repelling branch of the "slow curve". Assuming that the turning point is degenerate (or non-generic), we apply a correspondence presented in a recent paper. This application needs the definition of a family of functions ϕ that is studied in a first part. Then, we use the correspondence is used to compute the asymptotic expansion in the powers of the small parameter for the canard solution.