The primary driving force for the impending threat of global warming is the heightened concentration of carbon dioxide ( \(CO _2\) ) in the atmosphere. In this research work, a mathematical model has been developed to investigate the impact of both human activities and forest biomass on the dynamics of atmospheric carbon dioxide. This model assumes that the concentration of \(CO _2\) in the atmosphere rises due to a combination of natural processes and human activities. Additionally, it posits that forest biomass and other natural sinks absorb atmospheric \(CO _2\) . The equilibria of the model have been determined, and their stability has been thoroughly examined. The analysis of the model reveals that an escalation in thermal plants or industries corresponds to a rise in atmospheric level of \(CO _2\) . Notably, the model analysis identifies that the deforestation rate either due to thermal plants or industries or both has destabilizing effects on the system’s dynamics, i.e., if these parameters surpass a certain threshold, the system loses its stability, potentially giving rise to periodic solutions through Hopf bifurcation. Also, it is found that transcritical bifurcation takes place between interior and forest biomass-free equilibria as the deforestation either due to industrial activities or thermal plants related activities increases. To validate the theoretical findings, numerical simulations have been conducted, providing additional support to the analytical findings and their future implications.
