Home > Articles > Published articles > Simultaneous Bifurcation of Limit Cycles and Critical Periods |
Date: | 2022 |
Abstract: | The present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. Together with the classical methods, we present an approach which uses the Lie bracket to address the simultaneity in some cases. This approach is used to find the bi-weakness of cubic and quartic Liénard systems, the general quadratic family, and the linear plus cubic homogeneous family. We finish with an illustrative example by solving the problem of simultaneous bifurcation of limit cycles and critical periods for the cubic Liénard family. |
Grants: | Agencia Estatal de Investigación PID2019-104658GB-I00 Ministerio de Educación, Cultura y Deporte FPU16/04317 Ministerio de Ciencia e Innovación CEX2020-001084-M Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 |
Note: | Altres ajuts: acords transformatius de la UAB |
Rights: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original. |
Language: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Subject: | Limit cycles ; Critical periods ; Simultaneous bifurcation |
Published in: | Qualitative theory of dynamical systems, Vol. 21, Issue 1 (March 2022) , art. 20, ISSN 1662-3592 |
35 p, 542.0 KB |