Evolution of harvesting in competitive population dynamics with spatial heterogeneity

Abstract

The study investigates the intricate interactions, particularly the antagonistic dynamics, between two entities inhabiting a nonhomogeneous circumstance subjected to harvesting pressures. We initiate our analysis by constructing a robust mathematical framework utilizing partial differential equations (PDEs) to model the behaviors of the two species. We rigorously demonstrate the substantiality and exclusivity of solutions to the formulated model. In this context, we establish pivotal conditions that facilitate species coexistence, as well as delineate scenarios wherein one species may exert competitive pressures sufficient to drive the other towards extinction. Additionally, we identify conditions that could culminate in the simultaneous extinction of both species. The findings yield a comprehensive relative analysis of two distinct harvesting levels, providing critical insights into their differential impacts on species dynamics. Furthermore, we substantiate our theoretical conclusions through a series of numerical simulations, which serve to validate our model and its implications.

J. Bangladesh Math. Soc. 45.1 (2025) 32–49