Localizing limit cycles : from numeric to analytical results
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Giacomini, Hector (Université de Tours (França). Laboratoire de Mathemátiques et Physique Théorique)
Grau, Maite (Universitat de Lleida. Departament de Matemàtica)

Imprint:	Cham, etc : Springer Nature Switzerland AG, cop. 2018
Description:	5 pàg.
Abstract:	This note presents the results of [4]. It deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Liénard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.
Grants:	Ministerio de Economía y Competitividad MTM2014-53703-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Note:	Presentation given by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2016 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), which was dedicated to the mathematical theory and applications of multiple scale systems and systems with hysteresis, and held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 13th to 17th, 2016
Rights:	Tots els drets reservats.
Language:	Anglès
Series:	Trends in mathematics. Research perspectives CRM Barcelona ; 10
Document:	Capítol de llibre ; recerca ; Versió acceptada per publicar
Subject:	Transversal curve ; Poincaré-Bendixson region ; Limit cycle ; Planar differential system
Published in:	Extended abstracts Summer 2016, slow-fast systems and hysteresis, theory and applications, 2015, p. 17-21, ISBN 978-3-030-01152-9

DOI: 10.1007/978-3-030-01153-6_2

Postprint 4 p, 235.4 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Books and collections > Book chapters