Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model

Boumediene Benyahia; Tewfik Sari; Boumediene Benyahia; Tewfik Sari

doi:10.3934/mbe.2020296

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5504-5533. doi: 10.3934/mbe.2020296

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Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model

Boumediene Benyahia ^{1
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Tewfik Sari ²

1.
Laboratoire d’Automatique de Tlemcen, Université de Tlemcen, Algeria
2.
ITAP, University of Montpellier, INRAE, Institut Agro, Montpellier, France

Received: 27 May 2020 Accepted: 31 July 2020 Published: 13 August 2020

This paper deals with a mathematical analysis of two-steps model of anaerobic digestion process, including dynamics of soluble microbial products (SMP). We propose to investigate effects of the new variable SMP on qualitative properties of the process in different generic cases. Equilibria of the model are graphically established considering qualitative properties of the kinetics and, their stability are proved theoretically and/or verified by numerical simulations. It will shown that the model has a rich qualitative behavior as equilibria bifurcation and multi-stability according to the considered bifurcation parameter.
- anaerobic digestion,
- bioprocess,
- equilibria bifurcation,
- modeling,
- stability,
- steady state analysis
Citation: Boumediene Benyahia, Tewfik Sari. Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5504-5533. doi: 10.3934/mbe.2020296

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Abstract

This paper deals with a mathematical analysis of two-steps model of anaerobic digestion process, including dynamics of soluble microbial products (SMP). We propose to investigate effects of the new variable SMP on qualitative properties of the process in different generic cases. Equilibria of the model are graphically established considering qualitative properties of the kinetics and, their stability are proved theoretically and/or verified by numerical simulations. It will shown that the model has a rich qualitative behavior as equilibria bifurcation and multi-stability according to the considered bifurcation parameter.

References

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