Limit Cycles of Polynomially Integrable Piecewise Differential Systems

Author:

García Belén1,Llibre Jaume2ORCID,Pérez del Río Jesús S.1,Pérez-González Set1ORCID

Affiliation:

1. Departamento de Matemáticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain

2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain

Abstract

In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals.

Funder

Spanish Agencia Estatal de Investigación

Agencia Estatal de Investigación

H2020 European Research Council

AGAUR

Acadèmia de Ciències i Arts de Barcelona

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference14 articles.

1. Filippov, A.F. (1988). Differential Equations with Discontinuous Right–Hand Sides, Kluwer Academic Publishers Group.

2. Andronov, A., Vitt, A., and Khaikin, S. (1966). Theory of Oscillations, Pergamon Press.

3. Di Bernardo, M., Budd, C.J., Champneys, A.R., and Kowalczyk, P. (2008). Piecewise-Smooth Dynamical Systems: Theory and Applications, Springer.

4. Simpson, D.J.W. (2010). Bifurcations in Piecewise-Smooth Continuous Systems, World Scientific.

5. Dynamics and bifurcations of nonsmooth systems: A survey;Makarenko;Physica D,2012

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