Discontinuity Induced Bifurcations in a Model of Saccharomyces cerevisiae

TL;DR

This paper analyzes a mathematical model of Saccharomyces cerevisiae growth, revealing how discontinuities induce bifurcations and oscillations, with classifications of complex bifurcation scenarios supported by bifurcation diagrams.

Contribution

It provides a detailed bifurcation analysis of a yeast growth model, highlighting the role of discontinuities in generating complex bifurcation phenomena.

Findings

Stable oscillations occur via Andronov-Hopf bifurcations.

Discontinuity-induced bifurcations are classified and explained.

Bifurcation diagrams are supported by unfolding of singularities.

Abstract

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.