Human population induced urban developments and their effects on temperature rise: a nonlinear mathematical model

Excessive infrastructural developments, driven by urbanization, have not only brought destruction of forests, but also exacerbated the temperature of cities (or towns) due to formation of urban heat islands. Keeping such an urban system in mind, a nonlinear dynamical model is formulated in the proposed work in terms of system of differential equations. The model, comprising of forest resources, human population, urban infrastructural developments and temperature as system variables, is formulated on the assumption that infrastructural developments, induced through human population, escalate temperature of the region at the cost of deforestation. The derived model is mathematically analyzed for qualitative properties of its equilibrium solutions, extending from their existences to stabilities. Further, to demonstrate the impact of parametric variations on dynamical behavior, the system is also investigated for transcritical and Hopf - bifurcations. Quantitative analysis is also being executed with available numerical data to substantiate qualitative findings and to determine sensitiveness of equilibrium values of model outcomes towards system parameters. The results reveal that any of the parameters, which directly or indirectly, responsible for escalation in temperature of the region can put the system in a state of periodic oscillations, arises through Hopf - bifurcation. Therefore, it is suggested to control urban infrastructural developments through implementation of government strategies, which should include check over illegal encroachment of forested land for infrastructural developments.