Delay differential equation model of forest biomass and competition between wood‐based industries and synthetic‐based industries

Wood plays a very important role for daily household needs. In this paper, we have taken three parameters, forest biomass density FB, wood‐based industries density WI, and synthetic‐based industries density SI in the proposed mathematical modeling. The forest biomass is assumed to grow logistically, which requires a fixed time to achieve full growth. The excessive cutting of wood for the growth of wood‐based industries not only depletes these forest resources, but there comes a delay in the growth of forest biomass as well. On the contrary, the growth of synthetic‐based industry is independent of forest biomass, yet there is a competition between wood‐based products and synthetic‐based products as per market demands. With the help of differential equation, we studied the stability of the system. Delay plays a significant role in the system to understand the complex behavior of the system about non‐zero equilibrium point. Hopf‐bifurcation observed and directional analysis is studied using normal form theory and manifold reduction. MATLAB software is used to graphical representation of the system.