Periodic solutions of a generalized Van der Pol-Mathieu differential equation

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Authors	KALAS Josef KADEŘÁBEK Zdeněk
Year of publication	2014
Type	Article in Periodical
Magazine / Source	Applied Mathematics and Computation
MU Faculty or unit	Faculty of Science
Citation
Doi	https://doi.org/10.1016/j.amc.2014.01.161
Field	General mathematics
Keywords	Van der Pol Mathieu equation; Periodic solutions; Quasiperiodic solutions; Averaging method; Method of complexification; Autonomous equations; Phase space analysis
Description	The generalized Van der Pol–Mathieu equation with a small parameter is studied. The existence of periodic and quasiperiodic solutions is proved using the averaging method, the method of complexification and phase space analysis of a derived autonomous equation. The results extend and generalize those of Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012).
Related projects:	Matematické struktury Kvalitativní vlastnosti řešení diferenciálních rovnic a jejich aplikace