Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1601-104
Keywords
Hopf bifurcation, limit cycle, averaging theory of third order
First Page
1053
Last Page
1071
Recommended Citation
BENDIB, E, BADI, S, & MAKHLOUF, A (2017). On the 3-dimensional Hopf bifurcation via averaging theory of third order. Turkish Journal of Mathematics 41 (4): 1053-1071. https://doi.org/10.3906/mat-1601-104
