On the hyperelliptic limit cycles of Lienard systems
- Liu, Changjian
- Chen, Guoting
- Yang, Jiazhong
DOIAbstract
In this paper we study hyperelliptic limit cycles of the Lienard systems x = y, y = - f(m)(x) y - g(n)(x), where, respectively, f(m)(x) and g(n)(x) are polynomials of degree m and n, g(n)(0) = 0. We prove that, if m >= 5 and m + 1 < n < 2m, then there always exist Lienard systems of the above form such that they have a hyperelliptic limit cycle. This gives a positive answer to the open problem posed in the paper by Yu and Zhang (2011 J. Math. Anal. Appl. 376 535-9). By combining all the results obtained up to now, we in fact give a complete classification of the hyperelliptic limit cycles of the Lienard systems: Lienard systems of the above form have hyperelliptic limit cycles only in the following cases: (i) m = 2, 3 and m +...
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