Planar pseudo-almost limit cycles and applications to solitary waves

• Bourama Toni ^[1]
  1. [1] Virginia State University

     Virginia State University

     Estados Unidos

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 15, Nº. 1, 2013, págs. 131-149
• Idioma: inglés
• DOI: 10.4067/S0719-06462013000100009
• Enlaces
  • Texto completo
• Resumen
  • español

    Investigamos la existencia de ciclos seudo-casi límites, una nueva clase de no-periodicidad en la interfaz de las teorías de ciclos límites y seudo-casi periodicidad. Determinamos condiciones de existencia de muchos sistemas, incluyendo algunas perturbaciones seudocasi periódicas del oscilador armónico y los sistemas de Liénard. Aplicamos las condiciones para derivar la existencia de ondas solitarias seudo-cuasi periódicas, primero perturbando y luego transformando algunas ecuaciones diferenciales parciales hiperbólicas y parabólicas a ecuaciones del tipo Liénard. También se incluyen preguntas abiertas sobre la co-existencia de ciclos límite y estrictamente pseudo-casi periódicos ciclos límite de partición del espacio de fases, y la existencia de isócrono pseudo-casi ciclos límite.

  • English

    We investigate the existence of pseudo-almost limit cycles, a new class of non-periodicity at the interface of the theories of limit cycles and pseudo-almost periodicity. We determine the conditions of existence for several systems including some pseudo-almost periodic perturbations of the harmonic oscillator and the renowned Liénard systems. We apply to derive the existence of pseudo-almost periodic solitary waves by perturbing first then transforming some hyperbolic and parabolic partial differential equations to Liénard-type equations. Included also are open questions on the co-existence of limit cycles and strictly pseudo-almost periodic limit cycles partitioning the phase space, and the existence of isochronous pseudo-almost limit cycles.

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