Partial linearization for planar nonautonomous differential equations

We prove a partial linearization theorem for planar nonautonomous differential equations with one center-like direction and one hyperbolic direction. Gap conditions are formulated in terms of the dichotomy spectral intervals. The result is applied to the Duffing–van der Pol oscillator under a nonaut...

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Bibliographic Details
Published in:Journal of Differential Equations 2015-03, Vol.258 (5), p.1618-1652
Main Authors: Bonckaert, P., De Maesschalck, P., Doan, T.S., Siegmund, S.
Format: Article
Language:English
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Summary:We prove a partial linearization theorem for planar nonautonomous differential equations with one center-like direction and one hyperbolic direction. Gap conditions are formulated in terms of the dichotomy spectral intervals. The result is applied to the Duffing–van der Pol oscillator under a nonautonomous parametric perturbation.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2014.11.007