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 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.Comment: 23 pages, 7 figure

BIODEGRADATION OF ACRYLIC PAINTS: PROCESS MODELLING OF BIOCIDE EFFECT ON BIOMASS GROWTH AT DIFFERENT TEMPERATURES

Abstract Acrylic paint, notwithstanding the attention paid during the production process, couldbe contaminated by bacteria. This is a consequence of microbiological residuals on the can, resulting in the alterationof paint characteristics. It is therefore necessary to provide an in-canpreservation of the paint by using a biocide.In this paper, the evolution of an in-can system, using a thermo-fluid dynamic model is presented; as a biocide, 2-methyl-4-isothiazolin-3-one, commercially known as MIT,was considered. The model was implemented on gPROMSsoftware and it was possible to determine the inhibitory concentration of the biocideinorder to guarantee both the protection of the can and the protection of thecover phase. To develop the model, kinetic parameters have been found by fitting available literature experimental data. As far as the thermodynamical parameters, theequilibrium between liquid and vapor phases was described bythe NRTLmodel (ASPEN Plus). The model has been validated through a comparison with experimental literature results using MIT alone and a mixture of biocides (MIT/BIT). The main results are that,at the maximum allowable concentration (100 ppm as imposed by law), the MIT biocide is able to protectthe paint for long periods, even when the temperature varies cyclically from 10 to 40°C