Exploring forest resources depletion through Markov switching analysis

Abstract

This paper develops a mathematical model to explore forest resource depletion, integrating the dynamics of forest growth, rapid industrialization, and demographic expansion. Unlike prior literature, which predominantly relies on deterministic frameworks, our approach employs stochastic mathematical techniques to embed regime switching within differential equations, driven by irreducible Markov chains with an ergodic stationary distribution. Initially, the deterministic core of the stochastic model, excluding Markov chains, is analyzed by identifying equilibrium points and assessing their asymptotic stability analytically. The well-posedness of the stochastic system with Markov switching is then established, proving the existence and uniqueness of a positive solution. The asymptotic dynamics are subsequently investigated to pinpoint critical thresholds governing resource depletion or sustainability. This pioneering use of stochastic calculus unveils complex interactions overlooked by traditional deterministic models, constituting the primary contribution of this work. Numerical simulations substantiate the theoretical findings, offering a precise quantitative depiction of the system’s behavior and confirming the analytical implications. The results provide a basis for sustainable management policies, recommending external regulatory actions and controlled population pressure to maintain ecological equilibrium and prevent resource depletion. The research underscores the importance of integrating such stochastic methods for more realistic ecological forecasting and policy-making.