Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation
Archivum Mathematicum (2016)
- Volume: 052, Issue: 1, page 49-70
- ISSN: 0044-8753
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topKadeřábek, Zdeněk. "Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation." Archivum Mathematicum 052.1 (2016): 49-70. <http://eudml.org/doc/276748>.
@article{Kadeřábek2016,
abstract = {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.},
author = {Kadeřábek, Zdeněk},
journal = {Archivum Mathematicum},
keywords = {Van der Pol-Mathieu equation; periodic solutions; autonomous system; generalized Hopf bifurcation; Bautin bifurcation; averaging method; limit cycles},
language = {eng},
number = {1},
pages = {49-70},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation},
url = {http://eudml.org/doc/276748},
volume = {052},
year = {2016},
}
TY - JOUR
AU - Kadeřábek, Zdeněk
TI - Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 1
SP - 49
EP - 70
AB - 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.
LA - eng
KW - Van der Pol-Mathieu equation; periodic solutions; autonomous system; generalized Hopf bifurcation; Bautin bifurcation; averaging method; limit cycles
UR - http://eudml.org/doc/276748
ER -
References
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- Verhulst, F., Nonlinear Differential Equations and Dynamical Systems, 2nd ed., Springer, 2006. (2006) MR1036522
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