Unveiling the dynamic interrelationship between urbanization and carbon emissions: an interactive nonlinear mathematical model

Land transformations for residential, commercial, industrial, and transportation purposes that come with urbanization appear as the most intensifying factor of carbon emissions in big cities and towns. Based on this aspect, a nonlinear mathematical model as a differential-equation system is proposed to better elucidate it by including human population, land urbanization, and carbon emissions as variables. The proposed mathematical model is mathematically investigated for the behavior of equilibrium solutions, their stabilities, and associated bifurcations with the help of qualitative properties of differential equations and their corresponding numerical simulations. From the analysis, it is inferred that the system may not exhibit feasibility and stability around the coexistence-equilibrium solutions, and, in turn, transcritical and Hopf-bifurcation appear. Thus, overgrowth in the human population and land transformations responsible for the escalation of carbon emissions may shift the system into a destabilized state with undamped periodic oscillations and threatened sustainability.