This paper deals with a model of a biochemical reactor system with distributed parameters and with a time delay in the growth response. Time delay has been introduced in microbial growth systems to explain the time lapse between the consumption of (liquid) substrate and its conversion to (solid) biomass. We study here the properties of the resulting system of partial functional differential equations. We first prove the existence, positivity, and a compactness property of the system trajectories. We then prove the existence of periodic solutions of the system for large values of the delay. Numerical simulations illustrate the existence of such solutions.
Drame, A. K., Dochain, D., Winkin, J. J., & Wolenski, P. R. (2012). Periodic trajectories of distributed parameter biochemical systems with time delay. Applied Mathematics and Computation, 218(14), 7395-7405. https://doi.org/10.1016/j.amc.2011.12.086