Slow divergence integrals in generalized Liénard equations near centers

• Main Authors: Renato Huzak, Peter De Maesschalck
• Format: Article
• Language: English
• Published: University of Szeged 2014-12-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: generalized liénard equations; limit cycles; slow divergence integral; slow-fast systems
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=3307

Using techniques from singular perturbations we show that for any $n\ge 6$ and $m\ge 2$ there are Liénard equations $\{\dot{x}=y-F(x),\ \dot{y}=G(x)\}$, with $F$ a polynomial of degree $n$ and $G$ a polynomial of degree $m$, having at least $2[\frac{n-2}{2}]+[\frac{m}{2}]$ hyperbolic limit cycles, where $[\cdot]$ denotes "the greatest integer equal or below".