| Volume 1, Number 3, 2011, Pages 299-313 DOI：10.11948/2011021 |
| Bifurcation of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems of degree 5 with a cusp |
| Ali Atabaigi,Hamid R. Z. Zangeneh |
| Keywords:Hyper-elliptic Hamiltonian system |
| Abstract: |
| This paper deals with small perturbations of a class of hyper-elliptic Hamiltonian system, which is a Li é nard system of the form \(\dot{x}=y,\) \(\;\dot{y}=Q_1(x)+\varepsilon yQ_2(x)\) with \(Q_1\) and \(Q_2\) polynomials of degree 4 and 3, respectively. It is shown that this system can undergo degenerated Hopf bifurcation and Poincar é bifurcation, which emerge at most three limit cycles for \(\varepsilon\) sufficiently small. |
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