Geodesic
Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation
Archivum mathematicum, Tome 52 (2016) no. 1, pp. 49-70.

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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 Kadeřábek (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.
DOI : 10.5817/AM2016-1-49
Classification : 34C05, 34C23, 34C25, 34C29, 34D05
Keywords: Van der Pol-Mathieu equation; periodic solutions; autonomous system; generalized Hopf bifurcation; Bautin bifurcation; averaging method; limit cycles 
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     title = {Bautin bifurgation of a modified generalized {Van} der {Pol-Mathieu} equation},
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Kadeřábek, Zdeněk. Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation. Archivum mathematicum, Tome 52 (2016) no. 1, pp. 49-70. doi : 10.5817/AM2016-1-49. http://geodesic.mathdoc.fr/articles/10.5817/AM2016-1-49/

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