Dynamical behaviour of single photobioreactor with variable yield coefficient

Md Shariful Islam; Touhid Hossain; Mir Shariful Islam; Bidyut Baran Saha

doi:10.1016/j.heliyon.2022.e12187

Dynamical behaviour of single photobioreactor with variable yield coefficient

Heliyon. 2022 Dec 10;8(12):e12187. doi: 10.1016/j.heliyon.2022.e12187. eCollection 2022 Dec.

Authors

Md Shariful Islam¹, Touhid Hossain¹, Mir Shariful Islam^{2

3

4}, Bidyut Baran Saha^{2

3}

Affiliations

¹ Department of Mathematics, University of Dhaka, Bangladesh.
² Mechanical Engineering Department, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan.
³ International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan.
⁴ Department of Oceanography, University of Dhaka, Bangladesh.

Abstract

Scholars studied chemostat model with variable yield coefficient and a growth rate in Monod expression for the existence of natural oscillations in a bioreactor. This article explores dynamical properties of a similar simple model, analytically and numerically, in which the growth rate is a modified Haldane expression. Study includes determination of analytic conditions for existence of steady-state washout and no washout solutions, optimization of the performance of the bioreactor when no washout solution occurs, stability of the optimized steady state solution, and the ranges of the parameter values for which natural oscillations (Hopf Bifurcation) take place. Investigation shows that it is possible to gain natural oscillations for much smaller values of the substrate concentration compared to Monod-based earlier works.

Keywords: Bifurcation; Bioreactor; Chemostat model; Modified haldane model; Residence time.