BAUTIN BIFURGATION OF A MODIFIED GENERALIZED VAN DER POL-MATHIEU EQUATION

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Authors	KADEŘÁBEK Zdeněk
Year of publication	2016
Type	Article in Periodical
Magazine / Source	Archivum Mathematicum
MU Faculty or unit	Faculty of Science
Citation
Web	https://eudml.org/doc/276748
Doi	http://dx.doi.org/10.5817/AM2016-1-49
Keywords	Van der Pol-Mathieu equation; periodic solutions; autonomous system; generalized Hopf bifurcation; Bautin bifurcation; averaging method; limit cycles
Description	The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kaderabek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed.
Related projects:	Kvalitativní vlastnosti řešení diferenciálních rovnic a jejich aplikace Matematické struktury