A class of quadratic system with six limit cycles
by Du Chaoxiong; Liu Yirong; Wang Qinlong
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 5, No. 3, 2015

Abstract: In this paper, the Hopf bifurcation for a class of three-dimensional quadratic system is investigated by making use of singular values methods. Studied system lies in symmetrical vector field with regard to planar y = x and it has two symmetrical singular points (1,2,1) and (2,1,1). We give the expressions of the first three focal values of the singular point (1,2,1) and show that each one of the two singular points (1,2,1) and (2,1,1) of the investigated system can become a fine focus of third order at the same time. Moreover, we obtain that each one of the two singular points (1,2,1) and (2,1,1) of the investigated system can bifurcate three small limit cycles under a certain coefficient's disturbed condition. In sum, six limit cycles can bifurcate from system (1). In terms of Hopf bifurcation of a three-dimensional quadratic system, our results are new and interesting.

Online publication date: Wed, 05-Aug-2015

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Dynamical Systems and Differential Equations (IJDSDE):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com