Authors:
Pallavi Bisht,Vikas Kumar,DOI NO:
https://doi.org/10.26782/jmcms.2026.07.00007Keywords:
Afforestation,Forest resource,Mathematical model,population pressure,Stability analysis,Industrialization.,Abstract
In this article, a nonlinear dynamical model is developed to study the combined effect of population pressure, urbanization, industrialization, residential land expansion, and afforestation efforts on forest resources dynamics. The governing dynamics of the system were represented by six nonlinear differential equations describing the interactions among forest resources, population pressure, urbanization, industrialization, residential land expansion, and afforestation efforts. The positivity and boundedness of the model solutions are established to ensure the biological validity of the system. Equilibrium points are identified, and sufficient conditions for feasibility and uniqueness of the interior equilibrium are discussed. Local stability of the equilibrium points is analysed through the Jacobian matrix, characteristic equation, and Routh-Hurwitz Stability criteria, while global stability is examined using a suitable Lyapunov function under appropriate parameter restrictions. Numerical simulations are carried out using the MATLAB ODE45 solver to validate the theoretical findings and to illustrate the long-term behaviour of the system. The results show that increased population pressure, urbanization, industrialization, and residential expansion significantly reduce forest resources, while afforestation efforts contribute positively to forest regeneration and restoring ecological balance. Global sensitivity analysis is also performed using Latin Hypercube Sampling and PRCC indices. The findings suggest that sustainable forest management requires controlling anthropogenic pressures along with strengthening afforestation programs. The findings provide important insights for environmental planners and policymakers to design effective forest conservation and sustainable development strategiesRefference:
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