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@article{1645579, author = {Kadeřábek, Zdeněk}, article_location = {Brno}, article_number = {1}, 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}, language = {eng}, issn = {1212-5059}, journal = {Archivum Mathematicum}, title = {BAUTIN BIFURGATION OF A MODIFIED GENERALIZED VAN DER POL-MATHIEU EQUATION}, url = {https://eudml.org/doc/276748}, volume = {52}, year = {2016} }
TY - JOUR ID - 1645579 AU - Kadeřábek, Zdeněk PY - 2016 TI - BAUTIN BIFURGATION OF A MODIFIED GENERALIZED VAN DER POL-MATHIEU EQUATION JF - Archivum Mathematicum VL - 52 IS - 1 SP - 49-70 EP - 49-70 PB - Masarykova univerzita SN - 12125059 KW - Van der Pol-Mathieu equation KW - periodic solutions KW - autonomous system KW - generalized Hopf bifurcation KW - Bautin bifurcation KW - averaging method KW - limit cycles UR - https://eudml.org/doc/276748 L2 - https://eudml.org/doc/276748 N2 - 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. ER -
KADEŘÁBEK, Zdeněk. BAUTIN BIFURGATION OF A MODIFIED GENERALIZED VAN DER POL-MATHIEU EQUATION. \textit{Archivum Mathematicum}. Brno: Masarykova univerzita, 2016, roč.~52, č.~1, s.~49-70. ISSN~1212-5059. Dostupné z: https://dx.doi.org/10.5817/AM2016-1-49.
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