Hopf Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center

  • Ji Hua WangEmail author


This paper is concerned with small quadratic perturbations to one parameter family of generic reversible quadratic vector fields with a simple center. The first objective is to show that this system exhibits two small amplitude limit cycles emerging from a Hopf bifurcation. The second one we prove that the system has no limit cycle around the weak focus of order two. The results may be viewed as a contribution to proving the conjecture on cyclicity proposed by Iliev (1998).


Quadratic reversible system limit cycle weak focus Hopf bifurcation 

MR(2010) Subject Classification

34C07 34C08 34C23 37G15 


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The author would like to thank the referees for their valuable comments and corrections which improve the presentation of the paper.


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© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of MathematicsSun Yat-sen UniversityGuangzhouP. R. China

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