Sewing limit cycles for piecewise smooth systems with two linear centers and a coupled rigid center

Warley M. Batista, Jaume Llibre and Durval J. Tonon

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 17-25

Abstract: In this paper we provide an upper bound for the maximum number of limit cycles that two classes of planar piecewise smooth systems formed by three centers separated by two parallel lines can exhibit. So we have solved the extension of the 16th Hilbert problem for these two classes of piecewise smooth systems, that consists in providing a uniform upper bound for the maximum number of limit cycles that these two classes of differential systems can exhibit. The centers in the left and in the central parts are arbitrary linear centers, and the one on the right part is a rigid center ẋ=−y+xP(x,y),ẏ=x+yP(x,y), being the polynomial P(x,y) either λ+a10x+a01y or λ+a20x2+a11xy+a02y2, providing the two classes studied. In the first case the upper bound for the maximum number of limit cycles is eleven and in the second case such an upper bound is four.

Keywords: Piecewise smooth systems; Linear center; Rigid center; Limit cycle; Coupled centers (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475426001357
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:17-25

DOI: 10.1016/j.matcom.2026.04.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().