On the invariant rational curves of a certain family of polynomial differential equations

• Homero Díaz-Marín ^[1] ; Osvaldo Osuna ^[1]
  1. [1] Universidad Michoacana
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 56, Nº. 1, 2022, págs. 93-111
• Idioma: inglés
• DOI: 10.15446/recolma.v56n1.105621
• Títulos paralelos:
  • Sobre las curvas racionales invariantes de cierta familia de ecuaciones diferenciales
• Enlaces
  • Texto completo
• Resumen
  • español

    En este trabajo presentamos condiciones necesarias y suficientes para determinar si los ciclos límite de ciertas ecuaciones diferenciales en el plano son algebraicos o no. Particularmente, obtenemos criterios para que ciclos límite de ciertas ecuaciones derivadas de modelos depredador - presa con ciertos funcionales racionales de respuesta sean necesariamente óvalos trascendentes.

  • English

    In this work, we present sufficient conditions to determine if the limit cycles of certain differential systems in the plane are algebraic or not. In particular, we obtain criteria such that the limit cycles of equations derived from predatory prey models with rational functional response are necessarily transcendental ovals.

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