DETAILED STUDY OF LIMIT CYCLES AND GLOBAL BIFURCATIONS IN A CIRCADIAN RHYTHM MODEL

DOI10.1142/S0218127406014848zbMath1111.37067OpenAlexW2152830022MaRDI QIDQ5484862

András Volford, Peter L. Simon

Publication date: 21 August 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127406014848

zbMATH Keywords

saddle-node bifurcationHopf bifurcationparametric representation methodtwo-codimensional bifurcations

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Protein sequences, DNA sequences (92D20) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) General biology and biomathematics (92B05)

Related Items (4)

Limit Cycles and Bifurcations in a Biological Clock Model ⋮ Analysis of the biological clock of Neurospora ⋮ Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model ⋮ Dynamics of the Tyson-Hong-Thron-Novak circadian oscillator model

Cites Work

• Practical bifurcation and stability analysis: from equilibrium to chaos.
• Constructing global bifurcation diagrams by the parametric representation method
• Reconciling Mathematical Models of Biological Clocks by Averaging on Approximate Manifolds
• Numerical Methods for Bifurcations of Dynamical Equilibria
• Relationships between the discriminant curve and other bifurcation diagrams

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