A new result on averaging theory for a class of discontinuous planar differential systems with applications

Jackson Itikawa, Jaume Llibre, Douglas D. Novaes

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

Abstract

© European Mathematical Society. We develop the averaging theory at any order for computing the periodic solutions of periodic discontinuous piecewise differential system of the form dr/dθ= r'={F+(θ, r, ϵ) if 0≤ θ ≤ α, F-(θ, r, ϵ) if α ≤ θ ≤ 2π, where F±(θ, r, ϵ) = Σk i=1 ϵiF± i (θ, r) + ϵk+1R ± (θ, r, ϵ) with θ ϵ S1 and r ϵ D, where D is an open interval of ℝ+, and ϵ is a small real parameter. Applying this theory, we provide lower bounds for the maximum number of limit cycles that bifurcate from the origin of quartic polynomial differential systems of the form x = -y+xp(x, y), y = x+yp(x, y), with p(x, y) a polynomial of degree 3 without constant term, when they are perturbed, either inside the class of all continuous quartic polynomial differential systems, or inside the class of all discontinuous piecewise quartic polynomial differential systems with two zones separated by the straight line y = 0.
Original languageEnglish
Pages (from-to)1247-1265
JournalRevista Matematica Iberoamericana
Volume33
Issue number4
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Averaging method
  • Discontinuous differential system
  • Non-smooth differential system
  • Periodic solution
  • Uniform isochronous center

Fingerprint Dive into the research topics of 'A new result on averaging theory for a class of discontinuous planar differential systems with applications'. Together they form a unique fingerprint.

  • Cite this