Publication details

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

Authors

KADEŘÁBEK Zdeněk

Year of publication 2016
Type Article in Periodical
Magazine / Source Archivum Mathematicum
MU Faculty or unit

Faculty of Science

Citation
Web http://emis.muni.cz/journals/AM/16-1/am2548.pdf
Field General mathematics
Keywords Van der Pol-Mathieu equation; periodic solutions; autonomous system; generalized Hopf bifurcation; Bautin bifurcation; averaging method; limit cycles
Attached files
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 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.
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