Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 22, pp. 1-9.
Existence, uniqueness and other properties of the limit cycle
of a generalized Van der Pol equation
Xenakis Ioakim
Abstract:
In this article, we study the bifurcation of limit cycles from
the linear oscillator
,
in the class

where
is a small positive parameter tending to 0,
is even and
.
We prove that the above differential system, in the global plane
where
is even and
,
has a unique limit cycle. More specifically, the existence
of a limit cycle, which is the main result in this work,
is obtained by using the Poincare's method, and the uniqueness
can be derived from the work of Sabatini and Villari [6].
We also investigate and some other properties of this unique
limit cycle for some special cases of this differential system.
Such special cases have been studied by Minorsky [3] and
Moremedi et al [4].
Submitted June 22, 2013. Published January 10, 2014.
Math Subject Classifications: 34C07, 34C23, 34C25.
Key Words: Generalized Van der Pol equation; limit cycles; existence; uniqueness.
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Xenakis Ioakim
Department of Mathematics and Statistics
University of Cyprus
P.O. Box 20537, 1678 Nicosia, Cyprus
email: xioaki01@ucy.ac.cy
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