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Hopf Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center
Ji; Hua; WANG School; of; Mathematics; Sun; Yat-sen; University; Guangzhou; 510275; P.R.China
- quadratic
- reversible
- system
- limit
- cycle
摘要：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
摘要：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).
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