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Conference Papers Year : 2022

On a global stability of a two-step anaerobic digestion model

Abstract

In this work, we consider a two-step anaerobic digestion model where two microorganisms mutually cooperate by producing a substrate for the other's growth. The model is a four-dimensional system of ordinary differential equations. Since the system is conservative by considering the same dilution rates, we show that the fourth-order model can be reduced to a second-order model. Using the nullcline method, we show that the system can have up to four steady states for a general class of growth rates and we analytically determine the necessary and sufficient conditions for their existence according to the operating parameters. Using the method of the vector field, we determine the necessary and sufficient conditions of local and global asymptotic stability of all steady states of the reduced model. Using Thieme's result, we show that the global asymptotic behavior of the solutions of the reduced model is the same as that of the complete system. For specific growth rates of Monod type, the numerical simulations illustrate our mathematical analysis.
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Dates and versions

hal-03592332 , version 1 (01-03-2022)

Identifiers

  • HAL Id : hal-03592332 , version 1

Cite

Thamer Hmidhi, Radhouane Fekih-Salem. On a global stability of a two-step anaerobic digestion model. African Conference on Research in Computer Science and Applied Mathematics - CARI, Oct 2022, Hammamet, Tunisia. ⟨hal-03592332⟩

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TDS-MACS CARI2022
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