Discrete and ultradiscrete models for biological rhythms comprising a simple negative feedback loop

DOI10.1016/j.jtbi.2015.04.024zbMath1343.92034OpenAlexW2071263503WikidataQ39023087 ScholiaQ39023087MaRDI QIDQ738196

D. Kharzeev

Publication date: 16 August 2016

Published in: Journal of Theoretical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jtbi.2015.04.024

zbMATH Keywords

Neimark-Sacker bifurcationself-sustained oscillationsbiological rhythmsBoolean systemtropical discretization

Mathematics Subject Classification ID

Feedback control (93B52) Biological rhythms and synchronization (92B25)

Related Items (4)

Poincaré map approach to limit cycles of a simplified ultradiscrete Sel'kov model ⋮ Relation of stability and bifurcation properties between continuous and ultradiscrete dynamical systems via discretization with positivity: One dimensional cases ⋮ Types and stability of fixed points for positivity-preserving discretized dynamical systems in two dimensions ⋮ Ultradiscrete bifurcations for one dimensional dynamical systems

Cites Work

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• The secant condition for instability in biochemical feedback control. I: The role of cooperativity and saturability
• Passivity gains and the ``secant condition for stability
• Tropical discretization: ultradiscrete Fisher–KPP equation and ultradiscrete Allen–Cahn equation
• Simple mathematical models with very complicated dynamics

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