Harvesting of a predator-prey model with two effort functions and Holling type IV response function

Abstract

This study presents a mathematical model describing a three-species interaction in a marine ecosystem, involving two prey populations distributed across protected and exploited zones and a single predator species. The model is grounded in the Holling type IV functional response and incorporates two dynamic fishing effort functions governed by their own evolution equations. Unlike traditional static-effort frameworks, our approach reflects adaptive economic behavior over time. We investigate system dynamics through equilibrium analysis, local and global stability assessment using Lyapunov techniques, and derive an optimal harvesting strategy using Pontryagin’s Maximum Principle. Numerical simulations illustrate how spatial management and effort adaptation jointly influence sustainability outcomes, offering insights for marine resource governance under complex ecological and economic feedbacks.