Deleterious effects of legal and illegal logging on forestry biomass using a dynamical model.

The objective of the paper is to present a mathematical model that reflects the deleterious effect of illegal logging on forest biomass. In the model formulation, it is considered that the nutrients present in the soil helps to grow forestry biomass and on the other side, the forestry biomass is subjected to harvesting as a consequence of efforts are applied for industrial growth. From conservation perspective, in model formulation, the maximum extension of industries is observed in the presence of alternatives. The taxation scheme is also imposed on the industries as a control measure for conserving the forestry biomass. The model dynamics is analyzed using differential equation theory. During the study instability in the system is observed if the illegal logging of forestry biomass increases by a threshold. Instability in the system is shown by a particular set of parametric values. Bio- Economic equilibrium is obtained for the system under study. Pontryagin's principle is used to obtain the criteria for optimal tax policy. Analytical results are carried out in numerical simulation section to support the analytical findings using hypothetical data. Finally, sensitivity analysis of the hypothetical parameter is performed to show the behavior around interior equilibrium. [ABSTRACT FROM AUTHOR]