On the Uniqueness of Limit Cycles in a Generalized Liénard System

• Autores: Daoxiang Zhang, Ping Yan
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 3, 2019, págs. 1191-1199
• Idioma: inglés
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• Resumen

  • Kooij and Sun (J Math Anal Appl 208:260–276, 1997) proposed a theorem to guarantee the uniqueness of limit cycles for the generalized Liénard system dx/dt=h(y)-F(x),dy/dt=-g(x). We will give a counterexample to their theorem. Moreover, we shall give some sufficient conditions for the existence, uniqueness and hyperbolicity of limit cycles.