TY - JOUR
T1 - Periodic trajectories of distributed parameter biochemical systems with time delay
AU - Drame, A.K.
AU - Dochain, D.
AU - Winkin, J.J.
AU - Wolenski, P.R.
PY - 2012/3/15
Y1 - 2012/3/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84857446211&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2011.12.086
DO - 10.1016/j.amc.2011.12.086
M3 - Article
AN - SCOPUS:84857446211
SN - 0096-3003
VL - 218
SP - 7395
EP - 7405
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 14
ER -