Selma Ellaggoune, Sabrina Badi
Abstract:
For
small we consider the number of
limit cycles of the polynomial differential system
where
,
and
where
have degree
respectively for each
.
We provide an accurate upper bound of the maximum number of limit cycles that
this class of systems can have bifurcating from the periodic
orbits of the linear center
using the
averaging theory of first and second order. We give an example for which
this bound is reached.
Submitted October 1, 2016. Published December 14, 2016.
Math Subject Classifications: 34C25, 34C29, 37G15.
Key Words: Limit cycle; Lienard differential equation; averaging method.
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Selma Ellaggoune Laboratory of Applied Mathematics and Modeling University 8 Mai 1945 Guelma, Algeria email: sellaggoune@gmail.com | |
Sabrina Badi Laboratory of Applied Mathematics and Modeling University 8 Mai 1945 Guelma, Algeria email: badisabrina@yahoo.fr |
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