Cubic Liénard equations with quadratic damping having two antisaddles

• Autores: Robert E. Kooij, Chengzhi Li, Freddy Dumortier
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 1, Nº 2, 2000, págs. 163-210
• Idioma: inglés
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• Resumen

  • The paper deals with differential equations of the form $\dot{x} = y$, $\dot{y} = -g(x) -f(x)y$, with $f$ and $g$ polynomials of degree respectively two and three. They are called cubic Li\'enard equations with quadratic damping. Attention goes to the case in which the equations have three singular points of which one is a saddle and two are antisaddles. A lot of results are given on the upper-bound for the number of limit cycles, depending on the relative position of the zeros of $f$ and $g$ on the $x$-axis