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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

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

Published: 3 April 2013


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.

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