Cybernetic models are ODEs obtained by mass balances with the control/regulatory variables included. These regulatory variables named as cybernetic variables represent the regulatory actions taken by the cells. Cybernetic variables for induction/repression control the transcription of various enzymes which catalyze the metabolism of the uptake of a particular substrate. Cybernetic variables for inhibition/activation control the activity of the enzymes which metabolize a particular substrate. In this work, cybernetic model of a continuous culture of Klebsiella pneumoniae of Baloo and Ramkrishna (1991) which includes maintenance effects, is used. The inclusion of maintenance phenomena has made it more complicated. But this model with maintenance could very well describe the experimentally observed behavior of microorganisms at low dilution rates i.e. the biomass levels are very low and at zero dilution rates we have zero biomass values. This model is mathematically complicated as it contains non-differential max functions in the denominator of the cybernetic variables for inhibition/activation. A combinatorial approach proposed by Namjoshi and Ramkrishna (2001) is used to carry out the steady state analysis. The bifurcation analysis has been carried out for this model by Vasudeva Kumar et. al. (under review). We can detect washout/trivial and nontrivial steady state branches in bifurcation diagrams. Once, the trivial solutions are determined, it is possible to find out nontrivial solutions using branch point continuation from the transcritical bifurcation points where the trivial solutions intersect the non-trivial solutions. Finding the trivial steady states (washout solutions) is not possible analytically because of mathematical complexity of the model.
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