Analysis of biochemical reactions models with delays

DOI10.1016/j.jmaa.2010.10.038zbMath1205.92030OpenAlexW2017102883WikidataQ112197602 ScholiaQ112197602MaRDI QIDQ624556

Jan Poleszczuk, Marek Bodnar, Urszula Fory's

Publication date: 9 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.10.038

zbMATH Keywords

Hopf bifurcationasymptotic analysisdelay differential equationslocal and global stabilitybiochemical reaction

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Qualitative investigation and simulation of models involving functional-differential equations (34K60)

Related Items (12)

Time-delayed models of gene regulatory networks ⋮ An algorithm for Hopf bifurcation analysis of a delayed reaction-diffusion model ⋮ Stability of delay induced oscillations in gene expression of Hes1 protein model ⋮ On reduction of time-delay systems to a form with relative degree ⋮ The nature of Hopf bifurcation for the Gompertz model with delays ⋮ Qualitative and computational analysis of a mathematical model for tumor-immune interactions ⋮ Time delay-induced instabilities and Hopf bifurcations in general reaction-diffusion systems ⋮ Stability analysis of the family of tumour angiogenesis models with distributed time delays ⋮ Chaos in a tumor growth model with delayed responses of the immune system ⋮ Delays do not cause oscillations in a corrected model of humoral mediated immune response ⋮ Analysis of the Hopf bifurcation for the family of angiogenesis models ⋮ General model of a cascade of reactions with time delays: global stability analysis

Cites Work

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• Introduction to functional differential equations
• The nonnegativity of solutions to delay differential equations
• The role of dimerization in noise reduction of simple genetic networks
• Negativity of delayed induced oscillations in a simple linear DDE
• Evolutionary Games and Population Dynamics

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