Dynamics of the Higgins-Selkov and Selkov systems

DOI10.1016/j.chaos.2018.07.007zbMath1415.34058OpenAlexW2883658854WikidataQ129520201 ScholiaQ129520201MaRDI QIDQ2000318

Claudia Valls, Jaume Llibre, Joan C. Artés

Publication date: 28 June 2019

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2018.07.007

zbMATH Keywords

Selkov systemphase portraitPoincaré compactificationHiggins-Selkov system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Biochemistry, molecular biology (92C40) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

Qualitative study of the Selkov model ⋮ Final evolutions for simplified multistrain/two-stream model for tuberculosis and Dengue fever ⋮ Proof of Artés-Llibre-Valls's conjectures for the Higgins-Selkov and the Selkov systems ⋮ The limit cycles of the Higgins-Selkov systems ⋮ Unnamed Item ⋮ Phase portraits of the Higgins-Selkov system ⋮ Phase portraits of the Selkov model in the Poincaré disc

Cites Work

• Unnamed Item
• Uniform attractor of the non-autonomous discrete Selkov model
• Zero-Hopf bifurcation in the generalized Michelson system
• Semi-analytical solutions for the reversible Selkov model with feedback delay
• Recent advances on determining the number of real roots of parametric polynomials
• Qualitative analysis of steady states to the Sel'kov model
• Qualitative theory of planar differential systems
• Cubic Lienard equations with linear damping
• Classification of Continuous Flows on 2-Manifolds
• A SURVEY ON THE BLOW UP TECHNIQUE
• Global Structure of Ordinary Differential Equations in the Plane

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