Phase portraits of the Higgins-Selkov system

DOI10.3934/DCDSB.2021039zbMath1492.34056OpenAlexW3125762763MaRDI QIDQ2064494

Jaume Llibre, Marzieh Mousavi

Publication date: 6 January 2022

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2021039

zbMATH Keywords

limit cyclephase portraitPoincaré compactificationHiggins-Selkov system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (3)

Criteria for the nonexistence of periodic orbits in planar differential systems ⋮ Qualitative study of the Selkov model ⋮ The limit cycles of the Higgins-Selkov systems

Cites Work

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• Dynamics of the Selkov oscillator
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Global dynamics of a SD oscillator
• Proof of Artés-Llibre-Valls's conjectures for the Higgins-Selkov and the Selkov systems
• Recent advances on determining the number of real roots of parametric polynomials
• Dynamics of the Higgins-Selkov and Selkov systems
• Unbounded solutions of models for glycolysis
• Qualitative theory of planar differential systems
• A SURVEY ON THE BLOW UP TECHNIQUE
• Uniqueness of limit cycles in theoretical models of certain oscillating chemical reactions

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