An Elementary Study of a Class of Dynamic Systems with Two Time Delays

• Akio Matsumoto ^[1] ; Ferenc Szidarovszky ^[2]
  1. [1] Chuo University

     Chuo University

     Japón

     
  2. [2] University of Arizona

     University of Arizona

     Estados Unidos

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 3, 2012, págs. 103-113
• Idioma: inglés
• DOI: 10.4067/S0719-06462012000300007
• Enlaces
  • Texto completo
• Resumen
  • español

    Se realiza un análisis básico para determinar la estabilidad de la región de una cierta clase de ecuaciones diferenciales ordinaras con dos retrasos. Nuestro análisis se basa en la determinación de switches de estabilidad, en primer lugar cuando un autovalor es complejo puro, y luego revisando las condiciones para la pérdida o ganancia de estabilidad. En el caso de ambas pérdidas de estabilidad y ganancias de estabilidad, se obtiene la bifurcación de Hopf dando la posibilidad del nacimiento de ciclos límites.

  • English

    An elementary analysis is developed to determine the stability region of a certain class of ordinary differential equations with two delays. Our analysis is based on determining stability switches first where an eigenvalue is pure complex, and then checking the conditions for stability loss or stability gain. In the case of both stability losses and stability gains Hopf bifurcation occurs giving the possibility of the birth of limit cycles.

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