A Mathematical Model to Analyze the Dependence of Biomass on the Concentration of CO2

Scientists commonly use linear or bilinear functional responses to relate density of biomass and concentration of CO2 which depicts that density of biomass always increases as concentration of CO2 increases. A study shows that although CO2 provides food security to the biomass but up to some extent i.e. even CO2 is necessary for the growth of biomass but much higher concentration has negative effect on the growth of biomass (like soybean, corn). Here we have formulated and analysed a mathematical model taking clue from above result to study the dependence of biomass on the concentration of CO2. Conditions of local and global stability of interior equilibrium point, boundedness as well as persistence have been derived. Bifurcation analysis also has been done for the harvesting parameter. Results of the model resembles with the realistic behaviour of biomass with respect to CO2.