A Coordinate-Independent Version of Hoppensteadt’s Convergence Theorem

• Lax, Christian ^[1] ; Seliger, Katrin ^[1] ; Walcher, Sebastian ^[1]
  1. [1] Rheinisch-Westfälische Technische Hochschule Aachen University

     Rheinisch-Westfälische Technische Hochschule Aachen University

     Städteregion Aachen, Alemania

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 7-28
• Idioma: inglés
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• Resumen

  • The classical theorems about singular perturbation reduction (due to Tikhonov and Fenichel) are concerned with convergence on a compact time interval (in slow time) as a small parameter approaches zero. For unbounded time intervals Hoppensteadt gave a convergence theorem, but his criteria are generally not easy to apply to concrete given systems. We state and prove a convergence result for autonomous systems on unbounded time intervals which relies on criteria that are relatively easy to verify, in particular for the case of a one-dimensional slow manifold. As for applications, we discuss several reaction equations from biochemistry.