A mathematical model for the conservation of forestry biomass with an alternative resource for industrialization: a modified Leslie Gower interaction

Abstract

In this paper we have considered an age structure forestry biomass characterized as pre-mature and mature population stages and industrialization as a state variable. Industries prefer to harvest trees as its favorite raw material to be used, but it may depend on the alternatives in the shortage or low growth of mature trees, based on this assumption a modified Leslie–Gower interaction is considered for industrial growth. We have obtained sufficient conditions for the persistence and global attractivity of the system by applying the differential inequality theory. Theory of differential equation is used to establish the stability of the system. Pontryagin’s principle is applied for the optimal control and found the solution in the interior equilibrium. For the verification of analytic results we have done numerical simulation, sensitivity of parameters involved in interior equilibrium is also examined.