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

https://doi.org/10.51867/ajernet.maths.6.3.34

Authors

Keywords:

Stochastic differential equations (SDEs), Multi-patch ecosystem, Stochastic Lyapunov function, Predator-prey model

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.

Dimensions

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Published

2025-08-11

How to Cite

Mayabi, L. T., Angwenyi, D., & Oganga, D. (2025). Stochastic modelling of predator–prey dynamics in a three-patch ecosystem. African Journal of Empirical Research, 6(3), 413–427. https://doi.org/10.51867/ajernet.maths.6.3.34

Issue

Vol. 6 No. 3 (2025): Jul-Sep 2025

Section

Articles
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Copyright (c) 2025 Lucian Talu Mayabi, David Angwenyi, Duncan Oganga

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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