descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2020Embargo end date: 01 Jan 2019 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Dynamical Systems, volume 19, pages 1,343-1,371 (eissn: 1536-0040,

Authors: Douglas D. Novaes; Tere M. Seara; Marco A. Teixeira; Iris O. Zeli;

doi: 10.1137/19m1289959 , 10.48550/arxiv.1910.01954

arXiv: http://arxiv.org/abs/1910.01954

handle: 2117/329583

Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle

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Abstract

We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a simple two-fold cycle, which is characterized by a closed trajectory connecting a visible two-fold singularity to itself. It is shown that under certain generic conditions the perturbed system has sliding and crossing periodic solutions. In order to get our results, Melnikov's ideas were applied together with tools from the geometric singular perturbation theory. Finally, a study of a perturbed piecewise Hamiltonian model is performed.

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
Mathematical Sciences Research Institute
United States

Keywords

Differential equations, Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory, Periodic solutions, Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory, :37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory [Classificació AMS], :Matemàtiques i estadística [Àrees temàtiques de la UPC], Equacions diferencials, :34 Ordinary differential equations::34E Asymptotic theory [Classificació AMS], Dynamical Systems (math.DS), Sistemes dinàmics diferenciables, 34A36, 34C23, 37G15, Filippov systems, Sliding dynamics, Piecewise smooth differential systems, :34 Ordinary differential equations::34A General theory [Classificació AMS], FOS: Mathematics, Differentiable dynamical systems, Twofold singularity, Classificació AMS::34 Ordinary differential equations::34A General theory, Mathematics - Dynamical Systems

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