Global Asymptotic Stability of a Functional Differential Model with Time Delay of an Anaerobic Biodegradation Process

Authors

  • Milen Borisov Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev, Bl. 8 1113 Sofia, Bulgaria
  • Neli Dimitrova Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev, Bl. 8 1113 Sofia, Bulgaria
  • Mikhail Krastanov Faculty of of Mathematics and Informatics Sofia University 5, James Bourchier Blvd. 1164 Sofia, Bulgaria and Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev, Bl. 8 1113 Sofia, Bulgaria

DOI:

https://doi.org/10.55630/sjc.2017.11.9-29

Keywords:

bioreactor model, discrete delays, global stability, extremum seeking

Abstract

We study a nonlinear functional differential model of an anaerobic
digestion process of wastewater treatment with biogas production. The
model equations of biomass include two different discrete time delays. A
mathematical analysis of the model is completed including existence and
local stability of nontrivial equilibrium points, existence and boundedness
of the model solutions as well as global stabilizability towards an admissible
equilibrium point. We propose and apply a numerical extremum seeking
algorithm for maximizing the biogas flow rate in real time.
Numerical simulation results are also included.

ACM Computing Classification System (1998): D.2.6, G.1.10, J.2.

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Published

2017-11-27

Issue

Section

Articles