Piecewise linear differential systems with an algebraic line of separation

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dc.contributor.authorGasull, Armengol
dc.contributor.authorTorregrosa, Joan
dc.contributor.authorZhang, Xiang
dc.date.accessioned2021-09-21T17:37:00Z
dc.date.available2021-09-21T17:37:00Z
dc.date.issued2020-02-14
dc.description.abstractWe study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each n ∈ ℕ there exist piecewise linear differential systems separated by an algebraic curve of degree n having [n/2] hyperbolic limit cycles. Moreover, when n=2,3, we study in more detail the problem, considering a perturbation of a center and constructing examples with 4 and 5 limit cycles, respectively. These results follow by proving that the set of functions generating the first order averaged function associated to the problem is an extended complete Chebyshev system in a suitable interval.
dc.description.departmentMathematics
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationGasull, A., Torregrosa, J., & Zhang, X. (2020). Piecewise linear differential systems with an algebraic line of separation. Electronic Journal of Differential Equations, 2020(19), pp. 1-14.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14523
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectPiecewise linear differential system
dc.subjectAlgebraic separation
dc.subjectLimit cycle
dc.subjectECT-system
dc.titlePiecewise linear differential systems with an algebraic line of separation
dc.typeArticle

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