Heteroclinic Solutions in Singularly Perturbed Discontinuous Differential Equations

2023/02/24 by Flaviano Battelli, Battelli, Flaviano, Mičhal Fĕckan +3
Mathematics · Medicine · #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2302.12618

openalex publication_date 2023/02/24 · openalex created_date 2023/03/01 · openalex updated_date 2026/08/01

Abstract

We derive Melnikov type conditions for the persistence of heteroclinic solutions in perturbed slowly varying discontinuous differential equations extending to these equations similar results for continuous differential equations.

Related

• Permanency and bifurcations of bounded solutions near homocilincs with symetric eigenvalues
• On the Loss of Compactness in the Vectorial Heteroclinic Connection Problem
• Global continuation of homoclinic solutions
• Discontinuous Dynamical Systems: A tutorial on solutions, nonsmooth analysis, and stability
• Delayed loss of stability in singularly perturbed finite-dimensional gradient flows