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Limit Cycles of Continuous Piecewise Smooth Differential Systems

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Abstract

From the beginning of this century many articles have been published on the continuous and discontinuous piecewise differential systems specially in the plane. The big interest on these piecewise differential systems mainly comes from their increasing number of applications for modelling many natural phenomena. As it is usual in the planar differential systems one of the main difficulties for understanding their dynamics consists in controlling their limit cycles. The major part of papers studying continuous piecewise differential systems has an straight line as the line of separation between the differential systems forming the continuous piecewise differential systems. In this work we consider continuous piecewise differential systems separated by a circle and formed by one linear differential center and one quadratic differential center. We study the maximum number of limit cycles that such kind of continuos piecewise differential system can exhibit.

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Funding

The first author is partially supported by the Grant #2022/01375-7 and #2018/25575-0 of the São Paulo Research Foundation (FAPESP). The second author is partially supported by the Agencia Estatal de Investigación Grant PID2019-104658GB-I00, and the H2020 European Research Council Grant MSCA-RISE-2017-777911.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Baruque de Holanda, 651, Cidade Universitária Zeferino Vaz, Campinas, SP,  13083-859, Brazil

    Joyce A. Casimiro

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

    Jaume Llibre

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  1. Joyce A. Casimiro
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  2. Jaume Llibre
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Correspondence to Joyce A. Casimiro.

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Casimiro, J.A., Llibre, J. Limit Cycles of Continuous Piecewise Smooth Differential Systems. Results Math 78, 173 (2023). https://doi.org/10.1007/s00025-023-01948-w

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