Periodic trajectories of distributed parameter biochemical systems with time delay

A.K. Drame, D. Dochain, J.J. Winkin, P.R. Wolenski

Research output: Contribution to journal › Article

Abstract

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.
Original languageEnglish
Pages (from-to)7395-7405
Number of pages11
JournalApplied Mathematics and Computation
Volume218
Issue number14
DOIs
Publication statusPublished - 15 Mar 2012

Fingerprint

Periodic Trajectories
Time Delay
Time delay
Trajectories
Biomass
Differential equations
Computer simulation
Liquids
Partial Functional Differential Equation
Substrates
Positivity
Reactor
Compactness
Existence of Solutions
Periodic Solution
Substrate
Liquid
Trajectory
Numerical Simulation

Cite this

Drame, A.K. ; Dochain, D. ; Winkin, J.J. ; Wolenski, P.R. / Periodic trajectories of distributed parameter biochemical systems with time delay. In: Applied Mathematics and Computation. 2012 ; Vol. 218, No. 14. pp. 7395-7405.
@article{a2c5a933a7ba485c89541a395d1e9018,
title = "Periodic trajectories of distributed parameter biochemical systems with time delay",
abstract = "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.",
author = "A.K. Drame and D. Dochain and J.J. Winkin and P.R. Wolenski",
year = "2012",
month = "3",
day = "15",
doi = "10.1016/j.amc.2011.12.086",
language = "English",
volume = "218",
pages = "7395--7405",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",
number = "14",

}

Drame, AK, Dochain, D, Winkin, JJ & Wolenski, PR 2012, 'Periodic trajectories of distributed parameter biochemical systems with time delay', Applied Mathematics and Computation, vol. 218, no. 14, pp. 7395-7405. https://doi.org/10.1016/j.amc.2011.12.086

Periodic trajectories of distributed parameter biochemical systems with time delay. / Drame, A.K.; Dochain, D.; Winkin, J.J.; Wolenski, P.R.

In: Applied Mathematics and Computation, Vol. 218, No. 14, 15.03.2012, p. 7395-7405.

Research output: Contribution to journal › Article

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

VL - 218

SP - 7395

EP - 7405

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 14

ER -

Drame AK, Dochain D, Winkin JJ, Wolenski PR. Periodic trajectories of distributed parameter biochemical systems with time delay. Applied Mathematics and Computation. 2012 Mar 15;218(14):7395-7405. https://doi.org/10.1016/j.amc.2011.12.086

Access to Document