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- Title
On the 3-dimensional Hopf bifurcation via averaging theory of third order.
- Authors
BENDIB, Elouahma; BADI, Sabrina; MAKHLOUF, Amar
- Abstract
We apply the averaging theory of third order to polynomial quadratic vector fields in R3 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 ±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.
- Subjects
HOPF bifurcations; H-spaces; POLYNOMIAL approximation; QUADRATIC fields; PROBABILITY theory
- Publication
Turkish Journal of Mathematics, 2017, Vol 41, Issue 4, p1053
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1601-104