Turkish Journal of Mathematics
DOI
10.3906/mat-1601-104
Abstract
We apply the averaging theory of third order to polynomial quadratic vector fields in $\mathbb{R}^3$ to study the Hopf bifurcation occurring in that polynomial. Our main result shows that at most $10$ limit cycles can bifurcate from a singular point having eigenvalues of the form $\pm bi$ and $0$. We provide an example of a quadratic polynomial differential system for which exactly $10$ limit cycles bifurcate from a such singular point.
Keywords
Hopf bifurcation, limit cycle, averaging theory of third order
First Page
1053
Last Page
1071
Recommended Citation
BENDIB, ELOUAHMA; BADI, SABRINA; and MAKHLOUF, AMMAR
(2017)
"On the 3-dimensional Hopf bifurcation via averaging theory of third order,"
Turkish Journal of Mathematics: Vol. 41:
No.
4, Article 22.
https://doi.org/10.3906/mat-1601-104
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss4/22
