On the 3-dimensional Hopf bifurcation via averaging theory of third order

Elouahma BENDIB; Sabrina BADI; Ammar MAKHLOUF

Makale detayları

On the 3-dimensional Hopf bifurcation via averaging theory of third order

Yazarlar:

Elouahma BENDIB | Sabrina BADI | Ammar MAKHLOUF

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2017 Vol.41 Issue 4, pp.1053-1071

Belge Tipi:

Makale

Yayın Tarihi:

7/2017

Belge Dili:

Türkçe

Document ID (Org No.):

2000746032

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

We apply the averaging theory of third order to polynomial quadratic vector fields in R3R3\mathbb{R}^3 to study the Hopf bifurcation occurring in that polynomial. Our main result shows that at most 101010 limit cycles can bifurcate from a singular point having eigenvalues of the form ±bi±bi\pm bi and 000. We provide an example of a quadratic polynomial differential system for which exactly 101010 limit cycles bifurcate from a such singular point.

Makale detayları

On the 3-dimensional Hopf bifurcation via averaging theory of third order

Yazarlar: Elouahma BENDIB | Sabrina BADI | Ammar MAKHLOUF

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2017 Vol.41 Issue 4, pp.1053-1071

Belge Tipi: Makale

Yayın Tarihi: 7/2017

Belge Dili: Türkçe

Document ID (Org No.): 2000746032

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Elouahma BENDIB | Sabrina BADI | Ammar MAKHLOUF

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2017 Vol.41 Issue 4, pp.1053-1071

Belge Tipi:

Makale

Yayın Tarihi:

7/2017

Belge Dili:

Türkçe

Document ID (Org No.):

2000746032

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098