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Modelling and analysis: the effect of industrialization on diffusive forestry resource biomass in closed habitat. (English) Zbl 1095.92065

Summary: A mathematical model is proposed to study the depletion of forest biomass by different levels of industrialization in two different adjoining regions of the habitat leading to patchiness. In the model it is assumed that the density of forestry resource biomass is governed by the same logistic equation with the prescribed intrinsic growth rate and carrying capacity in both the regions. It is shown that the steady state distributions of the forestry resource as well as industrialization are positive, continuous and monotonic from one end to the other end of the linear closed habitat.
The model is analyzed by using the stability theory of differential equation. Further, it is shown that the steady state distributions of biomass in the two regions are stable under certain conditions and decrease as density of industrialization or rate of depletion due to industrialization increases in each of the two adjoining region.

MSC:

92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
35B35 Stability in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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