Analysis of a Bioreactor Model with Microbial Growth Phases and Spatial Dispersal
AbstractWe consider a batch mode bioreactor model proposed by Alt and Markov (2012). The model is developed using the fact that the bacterial growth undergoes four phases: lag, log, stationary and death phase. First, we modify the model by introducing additional (the so-called transport) terms to describe continuously stirred bioreactor dynamics. For this model we compute the equilibrium points and study their asymptotic stability. Some basic properties of the solutions like uniform boundedness and uniform persistence are also established. Then we extend the model by adding diffusion terms to the equations. The latter reaction-diffusion equations are studied numerically. Thereby, solutions in the form of travelling waves are found.
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