2013/12/10 by Tomáš Vejchodský, Vejchodský, Tomáš
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #34C15 #34C23 #80A30 #92B25 #92C45 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Photosynthetic Processes and Mechanisms #math.DS #msc:34C15 #msc:34C23 #msc:80A30 #msc:92B25 #msc:92C45
paper · pdf · doi:10.48550/arxiv.1312.2825
Presented at Equadiff 2013 conference in Prague. Accepted for publication in Mathematica Bohemica
arxiv created 2013/12/10 · openalex publication_date 2013/12/10 · arxiv updated 2013/12/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi steady state assumptions yields a simplified system that accurately agrees with the original system not only qualitatively but also quantitatively. We derive the proper size of the delays for a particular model of circadian rhythms and present numerical results showing the accuracy of this approach.