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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Periodic orbits and invariant cones in three-dimensional piecewise linear systems

Pages: 59 - 72, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.59

 
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Victoriano Carmona - Escuela Técnica Superior de Ingeniería, Departamento de Matemática Aplicada II, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain (email)
Emilio Freire - Escuela Técnica Superior de Ingeniería, Departamento de Matemática Aplicada II, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain (email)
Soledad Fernández-García - MYCENAE Project-Team, Paris-Rocquencourt Centre, Inria, Domaine de Voluceau BP 105, 78153 Le Chesnay Cedex, France (email)

Abstract: We deal with the existence of invariant cones in a family of three-dimensional non-observable piecewise linear systems with two zones of linearity. We find a subfamily of systems with one invariant cone foliated by periodic orbits. After that, we perturb the system by making it observable and non-homogeneous. Then, the periodic orbits that remain after the perturbation are analyzed.

Keywords:  Piecewise linear systems, periodic orbits, invariant manifolds, half-Poincaré maps, invariant cones.
Mathematics Subject Classification:  Primary: 34C25, 34C45; Secondary: 34C23, 37G15.

Received: July 2013;      Revised: May 2014;      Available Online: August 2014.

 References