An Improved Criterion for the Unique Existence of the Limit Cycle of a Liénard-type System with One Parameter

• Autores: Makoto Hayashi
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
• DOI: 10.1007/s12346-021-00463-z
• Enlaces
  • Texto completo
• Resumen

  • There are various types in generalized Liénard systems. In this paper, we treat a Liénard-type system in their paper. Though the existence of homoclinic orbits was discussed in their paper, our aim is to present a tool for the unique existence of limit cycles of the system with one parameter. It is an improvement of the criterion in Hayashi (Adv Dyn Syst Appl 14:179–187, 2019). As applications, the examples in the above paper of Hayashi or Villari and Zanolin (Dyn Syst Appl 25:321–334, 2016) are investigated under the more small parameter for the uniqueness of the limit cycle.

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