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

• Autores: Liz Eduardo, Sebastián Buedo-Fernández
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 3, 2019, págs. 813-824
• Idioma: inglés
• DOI: 10.1007/s12346-018-00314-4
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• Resumen

  • 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.