Logistic growth vs regrowth model with delay for the harvesting of vegetation biomass with its effects on CO2

Abstract

In this paper, nonlinear mathematical models have been proposed for comparative study of dynamics of CO₂ with respect to vegetation biomass considering different growths of vegetation biomass, such as logistic, regrowth and regrowth with delay. Here we have considered harvesting of vegetation biomass due to external factors. Conditions for boundedness, local and global stability of equilibrium points and persistence has been derived for the models. Numerical simulations has been carried out to support analytical results and analyse bifurcation  with respect to parameters(growth rates, catchability coefficient and depletion rate of CO₂ due to vegetation biomass). Model analysis reveals that, as compared to logistic growth, regrowth allows us a large span for harvesting in which system remains stable. Model analysis also shows that the model in which we have considered regrowth, density of vegetation biomass and concentration of CO₂ bifurcate negligibly with respect to different parameters as compared to logistic growth. Since often there exist a time lag for regrowth so we have also calculated critical value of lag after which system get unstabilized.