Comparative study of the effects of different growths of vegetation biomass on CO2 in crisp and fuzzy environments

Abstract

AbstractIn this paper, three fuzzy nonlinear mathematical models, corresponding to crisp models described in Devi and Gupta (2018), are formulated to study the comparative behavior of carbon dioxide concerning vegetation biomass in crisp and fuzzy environments. Logistic growth and regrowth of vegetation biomass are considered in the first two models, and delay is incorporated in the regrowth of vegetation biomass in the third one. Conditions for boundedness and persistence of the solutions, the existence of equilibrium points, and the stability of equilibrium points are carried out for each model. We also derived the formula for the critical value of time delay. Further, we also analyzed the existence, stability, and direction of the Hopf bifurcation. Numerical simulations were performed to complement analytical findings and to see the comparison between crisp and fuzzy environments. In fuzzy environment, it is observed that increment in the minimum value of regrowth rate shifts the destabilizing value of delay forward while if the maximum value of regrowth rate decreases, variables will become unstable before the estimated time. The overall analysis demonstrates that the behavior of the models in crisp and fuzzy environments is quite different.Recommendations for resource managers An increasing level of CO2 is the major factor for greenhouse effect, therefore to reduce the destructive effects of global warming, implementation of policies related to mitigation of the atmospheric CO2 is of paramount importance. Vegetation biomass has considerable regrowth rate as compared with the rest of the plants. But, there is some time lag in the process of regrowth, therefore for the growth rate of vegetation biomass regrowth with delay must be considered to avoid the fluctuations in the results. In the real world, the biological parameters are not always fixed because they vary according to the environment. So, scientists should consider fuzzy parameters for more precise results.