Discontinuity Induced Bifurcations in a Model of Saccharomyces cerevisiae

Details Discontinuity Induced Bifurcations in a Model of Saccharomyces cerevisiae Discontinuity Induced Bifurcations in a Model of Saccharomyces cerevisiae

2008-07-01

arxiv.org/abs/0807.0249v1

Math. Biosci. 218:40-49 (2009)

Nonlinear Sciences

Chaotic Dynamics

23 pages, 7 figures

Scientific paper

10.1016/j.mbs.2008.12.005

We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones and D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotech., 71:105-131, 1999]. Stable oscillations arise via Andronov-Hopf bifurcations and exist for intermediate values of the dilution rate as has been noted from experiments previously. A variety of discontinuity induced bifurcations arise from a lack of global differentiability. We identify and classify discontinuous bifurcations including several codimension-two scenarios. Bifurcation diagrams are explained by a general unfolding of these singularities.

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