The rising level of atmospheric carbon dioxide (CO2\documentclass[12pt]{minimal}
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\begin{document}$$CO _{2}$$\end{document}) gas is a matter of concern due to its impact on global climate change. The accomplishment of the goal of climate change mitigation requires a reduction in the CO2\documentclass[12pt]{minimal}
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\begin{document}$$CO _{2}$$\end{document} concentration in near future. The forest management programs offer an avenue to regulate atmospheric CO2\documentclass[12pt]{minimal}
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\begin{document}$$CO _{2}$$\end{document} levels. This paper presents a four-dimensional nonlinear mathematical model to study the impact of forest management policies on the mitigation of atmospheric CO2\documentclass[12pt]{minimal}
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\begin{document}$$CO _{2}$$\end{document} concentrations. It is assumed that forest management programs are applied according to the difference of forest biomass density from its carrying capacity. The forest management programs are assumed to work twofold: first, they increase the forest biomass and secondly they reduce the deforestation rate. Model analysis shows that the atmospheric level of CO2\documentclass[12pt]{minimal}
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\begin{document}$$CO _{2}$$\end{document} can be effectively curtailed by increasing the implementation rate of forest management options and their efficacy. It is found that as the deforestation rate coefficient exceeds a critical value, loss of stability of the interior equilibrium state occurs and sustained oscillations arise about interior equilibrium through Hopf-bifurcation. The stability and direction of bifurcating periodic solutions are discussed using center manifold theory. Further, it is observed that the amplitude of periodic oscillation dampens as the maximum efficacy of forest management programs to reduce the deforestation rate increases and above a critical value of the maximum efficacy of forest management programs, the periodic oscillations die out and the interior equilibrium becomes stable. The strategies for the optimal control of CO2\documentclass[12pt]{minimal}
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\begin{document}$$CO _{2}$$\end{document} concentration while minimizing the execution cost of forest management programs are also investigated using the optimal control theory. The theoretical results are demonstrated via numerical simulations.
