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A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System

Published online by Cambridge University Press:  20 November 2018

Chengzhi Li ,
Christiane Rousseau  and
Xian Wang
Chengzhi Li
Affiliation:
Department of mathematics, peking university, beijing, PRC
Christiane Rousseau
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128 Succ. A, Montréal Qué., H3C 3J7, Canada
Xian Wang
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, PRC
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Abstract

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We show that the Bogdanov-Takens system has at most one limit cycle. Similarly we show that the maximum number of limit cycles in the universal unfolding of the symmetric cusp of order 2 (resp. 3) is one (resp. 2). The proof uses the elementary technique of Liénard's equation, yielding a global result for all values of the parameters.

Keywords

34C0534C3539
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 84 - 92
Copyright
Copyright © Canadian Mathematical Society 1990

References

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