Modeling of global warming effect on the melting of polar ice caps with optimal control analysis

Abstract

This paper describes the impact of increasing carbon dioxide gas emissions on the growing threat of global warming and its effect on melting polar ice caps using a mathematical model. The stability analysis of three equilibria, namely human and forest absence, forest absence, and co-existence is presented in which all of the equilibria are conditionally stable. Further, the optimal control problem is formulated in the form of clean technological options and reforestation as control variables. The control variable problem is solved analytically through Pontryagin's Maximum Principle. The simulation shows that the combination of two controls give a significant impact to reduce the concentration of carbon dioxide and the rate of melting polar ice caps.