Stochastic modelling of predator–prey dynamics in a three-patch ecosystem

Abstract

This study presents a stochastic predator-prey model in a three-patch ecosystem, motivated by cage-based fish farming. Each patch hosts prey and predator populations, with inter-patch prey migration and unbounded variations in the population represented by stochastic terms. The model integrates logistic prey growth, predation, and mortality within a coupled system of stochastic differential equations. We assess stochastic stability using stochastic Lyapunov function methods. Numerical simulations confirm that when predator efficiency ei < 1, the total population remains bounded, indicating stability. However, for ei > 1, the system becomes unstable. The model also demonstrates that prey populations remain viable under low harvesting rates (ν1 = ν2 = ν3 = 0.02) and moderate noise intensities (0.10 ≤ σ ≤ 0.90). This work contributes to sustainable resource management by offering a robust framework for modeling predator-prey interactions in multi-patch environments.