Depletion and Conservation of Forestry Resources: A Mathematical Model
A mathematical model to study the depletion and conservation of forestry biomass in presence of industrialization is proposed and analyzed. In the modeling process, it is assumed that due to forestry biomass industries migrate in the region under consideration and their growth increases due to the availability of forestry biomass. It is also assumed that both the intrinsic growth rate and carrying capacity of forestry biomass depend on industrialization and technological efforts. The model analysis shows that the increase in carrying capacity of forestry biomass due to technological efforts has destabilizing effect. It is found that, by taking growth rate coefficient of carrying capacity of forestry biomass due to technological efforts as a bifurcation parameter, periodic solutions may arise through Hopf-bifurcation. Further, using center manifold theory, the direction and stability of periodic solutions have also been discussed. Numerical simulation is performed to support analytic results.
mathematical model forestry biomass industrialization stability hopf-bifurcation