A mathematical model for the conservation of forestry resources with two discrete time delays

Abstract

Forests are very important for the life on the planet earth. Now-a-days, depletion of forestry resources is a serious problem across the world and there is a need to make some efforts to conserve them. For this, in the present study, we have formulated a nonlinear mathematical model to assess the effect of applied technological efforts on the conservation of forestry resources with two discrete time delays. The first time delay is involved in applying technological efforts whereas the second one is responsible for the visibility of applied technological efforts on the growth of forestry resources. The conditions for local stability are obtained and it is shown that periodic solutions arise through Hopf-bifurcation as the time delay crosses some threshold value. Further, it is noted that the stable equilibrium may become unstable due to the increase in the value of second delay parameter. Numerical simulation is also performed to support the analytically obtained results.