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The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems

Part of: Qualitative theory

Published online by Cambridge University Press:  20 November 2017

Jaume Llibre  and
Xiang Zhang
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain ([email protected])
Xiang Zhang
Affiliation:
Department of Mathematics, MOE–LSC, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China ([email protected])
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Abstract

We provide sufficient conditions for the non-existence, existence and uniqueness of limit cycles surrounding a focus of a quadratic polynomial differential system in the plane.

Keywords

quadratic systemsquadratic polynomial differential systemlimit cycles

MSC classification

Primary: 34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
Secondary: 34C05: Location of integral curves, singular points, limit cycles
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 1 , February 2019 , pp. 1 - 14
Copyright
Copyright © Royal Society of Edinburgh 2017 

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