Mathematical Modeling of Ecosystem Resilience under Random Environmental Perturbations
Abstract: This paper develops a stochastic di?erential equation (SDE) framework for quantifying ecosystem resilience under random environmental perturbations. Starting from a deterministic Lotka-Volterra predator-prey system with Holling Type II functional response, we introduce multiplicative noise terms via Itô's formula and derive conditions for mean-square and almost-sure stability. A dimensionless Resilience Index R(σ) = 1 - σ2/(2λ0) is proposed, where λ0 > 0 is the dominant Lyapunov exponent of the deterministic equilibrium and σ is the noise intensity. A critical noise threshold σc = √2λ0 is identified beyond which the ecosystem loses stability. Numerical simulations using the Euler-Maruyama scheme confirm theoretical predictions and illustrate phase-portrait collapse, resilience decay, and stochastic trajectory divergence.
Keywords: Ecosystem resilience, stochastic di?erential equations, Itô calculus, Lyapunov exponent, predator-prey model, Holling Type II, mean-square stability, environmental noise
How to Cite?: Om Kumar, "Mathematical Modeling of Ecosystem Resilience under Random Environmental Perturbations", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 262-270, https://www.ijsr.net/getabstract.php?paperid=SR26704042037, DOI: https://dx.doi.org/10.21275/SR26704042037