Algebraic Limit Cycles
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2025
Abstract:	In the qualitative theory of differential equations in the plane ℝ2, one of the most difficult objects to study is the existence of limit cycles. Here, we summarize some results and open problems on the algebraic limit cycles of the planar polynomial differential systems. More precisely, (i) we study the algebraic limit cycles of the polynomial differential systems of degree 2; (ii) we provide the maximum number of generic algebraic limit cycles that the polynomial differential systems of degree n can exhibit; (iii) we show using the algebraic limit cycles that any finite configuration of limit cycles can be realized by some polynomial differential system; and (iv) we provide the maximum number of algebraic limit cycles formed by circles that a polynomial differential system of degree n can exhibit.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic limit cycle ; Limit cycle ; Polynomial vector field ; Quadratic polynomial vector field
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 35, Num. 14 (November 2025) , art. 2540008, ISSN 1793-6551

DOI: 10.1142/S0218127425400085

Available from: 2026-11-30 Postprint 14 p, 524.3 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles