Optimizing industrial growth through alternative forest biomass resources: A mathematical model using DDE

Abstract

Abstract This paper focuses on the classification of forest biomass into two categories: premature and mature forest biomass. The third variable considered is industrialization. The growth of the wood-based industry is believed to be closely tied to the population of mature forest biomass. Any scarcity of the mature population could have a negative impact on industrialization. So, pre-mature forest biomass is provided as an alternative for industrial growth. The industrialization growth is assumed to be based on a modified Leslie-Gower equation. The positivity and boundedness of the system are calculated using the comparison theorem. Stability analysis is done about nonzero equilibrium points with the help of the Routh-Hurwitz theorem. When there is no delay in the system, the system is stable. At τ< 1.8, the system shows asymptotic stability, but at τ ≥ 1.8, system shows Hopf-bifurcation and periods oscillations occur. Furthermore, sensitivity analysis is examined about different parameters of the systems. MATLAB is used to draw the numerical simulation.