%0 Journal Article
%T Dynamics and Hopf Bifurcation Analysis of a Chemostat Model with Modified Growth Rate and Variable Yield Coefficient
%A Md. Shariful Islam
%A Touhid Hossain
%A Mir Shariful Islam
%J Open Journal of Modelling and Simulation
%P 417-427
%@ 2327-4026
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojmsi.2022.104023
%X <span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">The objective of this study </span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">is </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">to
analyze a chemostat model of very simple type with the Haldane expression of
growth rate and a variable yield coefficient. The proposed modified model is
analyzed qualitatively and quantitatively. Analytic conditions for stability
and optimality are determined for washout and no washout equilibrium solutions.
One of the main focuses of the study is to determine parameter values for which
Hopf Bifurcations occur in a bioreactor. It has been shown that the maximum
stable non</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">-</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">washout equilibrium exits at a residence time under suitable parameter values.
Hopf bifurcation is observed at three different conditions of the parameters.
%K Chemostat
%K Residence Time
%K Hopf Bifurcation
%K Bioreactor
%K Growth Rate
%K Haldane Model
%K Yield Coefficient
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=120628