Gray, B.F. and Roberts, M.J. (1988) A Method for the Complete Qualitative Analysis of Two Coupled Ordinary Differential Equations Dependent on Three Parameters. Proceedings of the Royal Society A. Mathematical and Physical Sciences, 416, 361-389.
https://doi.org/10.1098/rspa.1988.0039

has been cited by the following article:

• TITLE: Dynamics and Hopf Bifurcation Analysis of a Chemostat Model with Modified Growth Rate and Variable Yield Coefficient

  AUTHORS: Md. Shariful Islam, Touhid Hossain, Mir Shariful Islam

  KEYWORDS: Chemostat, Residence Time, Hopf Bifurcation, Bioreactor, Growth Rate, Haldane Model, Yield Coefficient

  JOURNAL NAME: Open Journal of Modelling and Simulation, Vol.10 No.4, October 24, 2022

  ABSTRACT: The objective of this study is 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-washout equilibrium exits at a residence time under suitable parameter values. Hopf bifurcation is observed at three different conditions of the parameters.