Impact of Technological Efforts for Conservation and Growth of Forestry Biomass: A Modeling Study

A nonlinear mathematical model is developed to analyze the impact of technological interventions and conservation efforts on forestry biomass. The study introduces a three-dimensional biomass-technology-effort model that uniquely integrates technological interventions with conservation efforts. Local and global stability are established through Lyapunov functions, and quantitative benchmarks (equilibrium levels, parameter sensitivities) are derived. The model represents an autonomous system of non-linear ordinary differential equations consisting of relationships among dynamic variables. These variables are the density of forestry biomass, the magnitude of technology and the magnitude of effort like reforestation. The analysis showed that augmenting technology and reforestation efforts can measurably enhance long-term biomass. The explicit numerical outcomes: equilibrium biomass ≈139 tons/ha (87% of L=160), technology ≈168 (thousand USD), effort ≈671 (million USD). Doubling \(\lambda\) increases biomass by ~0.06 units and technology by ~167 units. Doubling s2 yields the largest biomass rise (~2.8 units in 50 years), while doubling \(\theta\) increases effort \(F\) by ~15-16 units. Sensitivity analysis confirms that biomass responds most strongly to s1 and s2, with \(\lambda\) and \(\theta\) mainly driving technology and effort. Lyapunov margins permit safe increase up to ≈7 times for \(\lambda\), \(\theta\), and s2. Model trajectories initiating from different points in the positive region converge to the nontrivial equilibrium, demonstrating its stability. The study provides concrete numerical benchmarks for policymakers: even modest increases in technology-driven conservation can yield measurable gains in biomass growth and improved resilience against anthropogenic pressures.