Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae.
We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones, D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotechnol. 71 (1999) 105-131]. 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.
Simpson
D J W
DJ
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, USA. simpson@colorado.edu
Kompala
D S
DS
Meiss
J D
JD
D001683:Biological Clocks / Q000502:physiology; D008954:Models, Biological; D012441:Saccharomyces cerevisiae / Q000254:growth & development*