Globally Asymptotically Stable Equilibrium Points in Kukles Systems

The problem of determining the basin of attraction of equilibrium points is of great importance for applications of stability theory. In this article, we address the global asymptotic stability problem of an equilibrium point of an ordinary differential equation on the plane. More precisely, we stud...

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Veröffentlicht in:Qualitative theory of dynamical systems Jg. 19; H. 3
Hauptverfasser: Dias, Fabio Scalco, Mello, Luis Fernando
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2020
Springer Nature B.V
Schlagworte:
Asymptotic properties
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Ordinary differential equations
Stability
Global asymptotic stability
Poincaré compactification
34D23
34A26
Kukles system
34D05
ISSN:1575-5460, 1662-3592
Online-Zugang:Volltext
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Zusammenfassung:The problem of determining the basin of attraction of equilibrium points is of great importance for applications of stability theory. In this article, we address the global asymptotic stability problem of an equilibrium point of an ordinary differential equation on the plane. More precisely, we study equilibrium points of Kukles systems from the global asymptotic stability point of view. First of all, we classify the Kukles systems satisfying the assumptions: the origin is the unique equilibrium point which is locally asymptotically stable, and the divergence is negative except possibly at the origin. Then, for each of such Kukles system, we prove that the origin is globally asymptotically stable. Poincaré compactification is used to study the systems on the complements of compact sets.
Bibliographie:ObjectType-Article-1
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ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-020-00432-y