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

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 di...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 18; no. 3; pp. 813 - 824
Main Authors Liz, Eduardo, Buedo-Fernández, Sebastián
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2019
Springer Nature B.V
Subjects
Asymptotic properties
Difference and Functional Equations
Difference equations
Differential equations
Dimensional stability
Dynamical Systems and Ergodic Theory
Economic analysis
Economic models
Formulas (mathematics)
Mathematical models
Mathematics
Mathematics and Statistics
Stability criteria
Discrete-time model
39A30
Global stability
Mackey–Glass equation
Schwarzian derivative
Primary 39A10
Gamma-model
Secondary 34K20
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Summary: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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-018-00314-4