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Bifurcation search via feedback loop breaking in biochemical signaling pathways with time delay
Author(s) -
Waldherr Steffen,
Dylus David,
Allgöwer Frank
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.383
Subject(s) - parameter space , bifurcation , control theory (sociology) , cascade , ordinary differential equation , computer science , feedback loop , control (management) , mathematics , differential equation , engineering , artificial intelligence , physics , nonlinear system , mathematical analysis , statistics , computer security , quantum mechanics , chemical engineering
We develop a method to locate bifurcations in time delay systems with a potentially high‐dimensional parameter space. It is based on the feedback loop breaking approach that we developed and applied earlier for bifurcation search in ordinary differential equations. The method is particularly suited for the analysis of biological networks, for example to determine which parameters are relevant for complex dynamical behavior in such networks. To illustrate the benefits that this approach yields for biological network analysis, we apply it to study the effect of parameter variations on oscillations in a model of the MAP kinase cascade with a time delay. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society