Dynamics analysis of an age distribution model of oscillating yeast cultures

The ability of an age-population balance model to capture experimentally observed oscillatory dynamics of continuous cultures of budding yeast was investigated through numerical simulations. Experiments with continuous yeast cultures have shown that several oscillatory modes can occur at the same operating condition, and that the mode attained depends on the start-up conditions. Numerical simulations of the model did reveal the existence of several stable periodic solutions. However, each occurred over a different range of dilution rates. Experiments also have shown that the steady state in continuous yeast cultures is stable, even under conditions that allow oscillatory dynamics. The stability of the steady state of the age population balance model under conditions that allow oscillatory dynamics was not resolved. The Jacobian matrix at the steady state is highly ill conditioned, with some eigenvalues very close to the imaginary axis. Using different integration routines to solve the model gave different results with regard to the stability of the steady state, one solver finding the steady state to be stable, another finding the steady state to be unstable.