Minimal sets in singularly perturbed systems with three time-scales

Authors

  • Pedro Toniol Cardin
  • Paulo Ricardo da Silva
  • Marco Antonio Teixeira

DOI:

https://doi.org/10.5540/03.2015.003.01.0003

Keywords:

Singular perturbations problems, three time scales

Abstract

In this work we study three time scale singular perturbation problems

"x

= f(x; "; ); y

= g(x; "; ); z

= h(x; "; );
where x = (x; y; z) ∈ Rn × Rm × Rp, " and are two independent small parameter (0 < ", ≪ 1), and f, g, h are Cr functions, with r ≥ 1. We establish conditions for the existence of compact invariant sets (singular points, periodic and homoclinic orbits) when "; > 0. Our main strategy is to consider three time scales which generate three different limit problems.

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Published

2015-08-25

Issue

Section

Análise Aplicada