Dynamics of the Higgins–Selkov and Selkov systems

Joan Carles Artés; Jaume Llibre; Claudià Valls

doi:10.1016/j.chaos.2018.07.007

Dynamics of the Higgins–Selkov and Selkov systems

Joan Carles Artés, Jaume Llibre, Claudià Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

© 2018 Elsevier Ltd We describe the global dynamics in the Poincaré disc of the Higgins–Selkov model x′=k0−k1xy2,y′=−k2y+k1xy2,where k0, k1, k2 are positive parameters, and of the Selkov model x′=−x+ay+x2y,y′=b−ay−x2y,where a, b are positive parameters. We determine the regions of initial conditions with biological meaning.

Original language	English
Pages (from-to)	145-150
Journal	Chaos, Solitons and Fractals
Volume	114
DOIs	https://doi.org/10.1016/j.chaos.2018.07.007
Publication status	Published - 1 Sep 2018

Keywords

Higgins–Selkov system
Phase portrait
Poincaré compactification
Selkov system

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title = "Dynamics of the Higgins–Selkov and Selkov systems",

abstract = "{\textcopyright} 2018 Elsevier Ltd We describe the global dynamics in the Poincar{\'e} disc of the Higgins–Selkov model x′=k0−k1xy2,y′=−k2y+k1xy2,where k0, k1, k2 are positive parameters, and of the Selkov model x′=−x+ay+x2y,y′=b−ay−x2y,where a, b are positive parameters. We determine the regions of initial conditions with biological meaning.",

keywords = "Higgins–Selkov system, Phase portrait, Poincar{\'e} compactification, Selkov system",

author = "Art{\'e}s, {Joan Carles} and Jaume Llibre and Claudi{\`a} Valls",

year = "2018",

month = sep,

day = "1",

doi = "10.1016/j.chaos.2018.07.007",

language = "English",

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journal = "Chaos, Solitons and Fractals",

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TY - JOUR

T1 - Dynamics of the Higgins–Selkov and Selkov systems

AU - Artés, Joan Carles

AU - Llibre, Jaume

AU - Valls, Claudià

PY - 2018/9/1

Y1 - 2018/9/1

N2 - © 2018 Elsevier Ltd We describe the global dynamics in the Poincaré disc of the Higgins–Selkov model x′=k0−k1xy2,y′=−k2y+k1xy2,where k0, k1, k2 are positive parameters, and of the Selkov model x′=−x+ay+x2y,y′=b−ay−x2y,where a, b are positive parameters. We determine the regions of initial conditions with biological meaning.

AB - © 2018 Elsevier Ltd We describe the global dynamics in the Poincaré disc of the Higgins–Selkov model x′=k0−k1xy2,y′=−k2y+k1xy2,where k0, k1, k2 are positive parameters, and of the Selkov model x′=−x+ay+x2y,y′=b−ay−x2y,where a, b are positive parameters. We determine the regions of initial conditions with biological meaning.

KW - Higgins–Selkov system

KW - Phase portrait

KW - Poincaré compactification

KW - Selkov system

U2 - 10.1016/j.chaos.2018.07.007

DO - 10.1016/j.chaos.2018.07.007

M3 - Article

VL - 114

SP - 145

EP - 150

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -