Open Access Research

Fast-slow dynamical approximation of forced impact systems near periodic solutions

Flaviano Battelli1 and Michal Fečkan2*

Author Affiliations

1 Dipartimento di Ingegneria Industriale e Scienze Matematiche, Marche Polytecnic University, Ancona, 60100, Italy

2 Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, Bratislava, 842 48, Slovakia

For all author emails, please log on.

Boundary Value Problems 2013, 2013:71  doi:10.1186/1687-2770-2013-71

Published: 3 April 2013

Abstract

We approximate impact systems in arbitrary finite dimensions with fast-slow dynamics represented by regular ODE on one side of the impact manifold and singular ODE on the other. Lyapunov-Schmidt method leading to Poincaré-Melnikov function is applied to study bifurcations of periodic solutions. Several examples are presented as illustrations of abstract theory.

MSC: 34C23, 34C25, 37G15, 70K50.

Keywords:
fast-slow dynamics; impact systems; bifurcations; periodic solutions; Poincaré-Melnikov method