A New Formula to Get Sharp Global Stability Criteria for One-Dimensional Discrete-Time Models

  1. Eduardo, Liz
  2. Buedo-Fernández, Sebastián
Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Ano de publicación: 2019

Volume: 18

Número: 3

Páxinas: 813-824

Tipo: Artigo

DOI: 10.1007/S12346-018-00314-4 DIALNET GOOGLE SCHOLAR

Outras publicacións en: Qualitative theory of dynamical systems

Resumo

We present a new formula that makes it possible to get sharp global stability results for one-dimensional discrete-time models in an easy way. In particular, it allows to show that the local asymptotic stability of a positive equilibrium implies its global asymptotic stability for a new family of difference equations that finds many applications in population dynamics, economic models, and also in physiological processes governed by delay differential equations. The main ingredients to prove our results are the Schwarzian derivative and some dominance arguments.

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