Forestry biomass conservation with synthetic industry: A mathematical model

In this paper, a mathematical model is proposed and analyzed considering four compartment as pre-mature trees, nature trees, wood based industries and alternative synthetic industries. It is assumed that the pre-mature trees grow logistically, and it requires a fixed amount of time for maturity, finally the mature trees are used by the wood based industries. Further assumed that the synthetic industries grow at a constant rate and there is a competition between these two types of industries. The behaviour of the system near all feasible equilibrium are studied and it is observed that the maturation delay of trees plays an important role and the system exhibits a Hopf-bifurcation about the non-trivial equilibrium with respect to the delay parameter. Numerical justification of the analytical results is also shown in the last section.