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Quadratic systems with a weak focus

Published online by Cambridge University Press:  17 April 2009

Zhang Pingguang  and
Cai Suilin
Zhang Pingguang
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou Zhejiang, Peoples Republic of China
Cai Suilin
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou Zhejiang, Peoples Republic of China
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Abstract

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In this paper we study the number and the relative position of the limit cycles of a plane quadratic system with a weak focus. In particular, we prove the limit cycles of such a system can never have (2, 2)-distribution, and that there is at most one limit cycle not surrounding this weak focus under any one of the following conditions:

(i) the system has at least 2 saddles in the finite plane,

(ii) the system has more than 2 finite singular points and more than 1 singular point at infinity,

(iii) the system has exactly 2 finite singular points, more than 1 singular point at infinity, and the weak focus is itself surrounded by at least one limit cycle.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 511 - 526
Copyright
Copyright © Australian Mathematical Society 1991

References

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