New lower bound for the Hilbert number in piecewise quadratic differential systems

Leonardo P.C. da Cruz, Douglas D. Novaes, Joan Torregrosa

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10 Citations (Scopus)

Abstract

© 2018 Elsevier Inc. We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by Hp(n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then Hp(2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center.
Original languageEnglish
Pages (from-to)4170-4203
JournalJournal of Differential Equations
Volume266
DOIs
Publication statusPublished - 15 Mar 2019

Keywords

  • First and second order perturbations of isochronous quadratic systems
  • Hilbert number for piecewise quadratic differential systems
  • Limit cycles in piecewise quadratic differential systems
  • Non-smooth differential system

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    da Cruz, L. P. C., Novaes, D. D., & Torregrosa, J. (2019). New lower bound for the Hilbert number in piecewise quadratic differential systems. Journal of Differential Equations, 266, 4170-4203. https://doi.org/10.1016/j.jde.2018.09.032