Planar S-systems: Global stability and the center problem

Balázs Boros; Josef Hofbauer; Stefan Müller; Georg Regensburger

doi:10.3934/dcds.2019029

Planar S-systems: Global stability and the center problem

Balázs Boros, Josef Hofbauer, Stefan Müller, Georg Regensburger

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles.

Original language	English
Pages (from-to)	707-727
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems - Series A
Volume	39
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2019029
Publication status	Published - Feb 2019

Austrian Fields of Science 2012

101004 Biomathematics

Keywords

Andronov-Hopf bifurcation
Bautin bifurcation
LAW
Power-law systems
center-focus problem
first integrals
focal values
global center
reversible systems
Focal values
Global center
Reversible systems
Center-focus problem
First integrals

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10.3934/dcds.2019029

http://aimsciences.org//article/id/49cb0104-c52a-4053-abd3-71935744f61a

Cite this

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title = "Planar S-systems: Global stability and the center problem",

abstract = "S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles.",

keywords = "Andronov-Hopf bifurcation, Bautin bifurcation, LAW, Power-law systems, center-focus problem, first integrals, focal values, global center, reversible systems, Focal values, Global center, Reversible systems, Center-focus problem, First integrals",

author = "Bal{\'a}zs Boros and Josef Hofbauer and Stefan M{\"u}ller and Georg Regensburger",

year = "2019",

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language = "English",

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pages = "707--727",

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AU - Boros, Balázs

AU - Hofbauer, Josef

AU - Müller, Stefan

AU - Regensburger, Georg

PY - 2019/2

Y1 - 2019/2

N2 - S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles.

AB - S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles.

KW - Andronov-Hopf bifurcation

KW - Bautin bifurcation

KW - LAW

KW - Power-law systems

KW - center-focus problem

KW - first integrals

KW - focal values

KW - global center

KW - reversible systems

KW - Focal values

KW - Global center

KW - Reversible systems

KW - Center-focus problem

KW - First integrals

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U2 - 10.3934/dcds.2019029

DO - 10.3934/dcds.2019029

M3 - Article

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VL - 39

SP - 707

EP - 727

JO - Discrete and Continuous Dynamical Systems - Series A

JF - Discrete and Continuous Dynamical Systems - Series A

IS - 2

ER -

Planar S-systems: Global stability and the center problem

Abstract

Austrian Fields of Science 2012

Keywords

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