Manisha Chaudhary and Joydip Dhar and Govind Prasad Sahu
Mathematical Model of Depletion of Forestry Resource Effect of Synthetic Based Industries
639 - 643
2013
7
4
International Journal of Biological and Ecological Engineering
https://publications.waset.org/pdf/16903
https://publications.waset.org/vol/76
World Academy of Science, Engineering and Technology
A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1 forest biomass free and wood industries free equilibrium; E2 wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopfbifurcation about the nontrivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.
Open Science Index 76, 2013