Dynamical analysis of chemostat models incorporating variable yield coefficient and substrate inhibition with recycling process - Mohd Sadiq, Ummalaisha Farhana (2021)
This research analyses chemostat models for microbial production. Chemostat is a tool that can be used for the continuous production of microbes under controlled conditions such as pH, temperature, light, and nutrients. This ability makes chemostat promising for the applications of microbes as renewable resources, microbial products and wastewater treatment. The dynamics of the chemostat can be described using the chemostat mathematical model. The microbial growth in the chemostat can be interpreted mathematically using the specific growth rate model. The growth of microbes chiefly depends on the concentration of the nutrient. However, the growth of microbes can be inhibited under a high concentration of nutrients. Therefore, in this thesis, Andrew’s growth model was considered to describe the inhibitory effect of high substrate concentration on the microbial growth in the chemostat model. The dependency of product yield towards the substrate concentration was also incorporated into the chemostat model. The performance of chemostat was also investigated with the influence of the recycling process. The stability and bifurcation analyses of the chemostat models were conducted to examine the dynamical behaviour of the steady-state of the chemostat system to identify the regions of parameters that generate oscillations of microbe population in the chemostat which occurs due to any changes in the stability of the steady-state of the system. There are two types of steady-states found which are washout steady-state and no washout steady-state. Washout steady-state means there is no growth of microbes occur in the reactor while no washout steady-state means there is growth of microbe occur in the chemostat. The steady-state solutions and their stability were determined as a function of residence time. The studies revealed the conditions to avoid the situation where no growth of microbes occurred in the chemostat. It was identified that there exists a parameters’ region that can generate stable limit cycle and also region of bistability of steady-states. The high value of recycling parameter increases the cell mass concentration in the chemostat.