Abstract

The main purpose of this paper is to study a simple open-access fishery model considering that the exploited resource is affected by the Allee effect, known as depensation in Fisheries Sciences and that the nominal fishing effort varies continuously over time. The system obtained modifies the well-known Smith model, one of the simplest bioeconomic models used in Renewable Resource Management. We show that the mathematical properties of the original model undergo a significant change since the equilibrium point 0,0 now turns out to be an attractor equilibrium point regardless of the parameter values. This is due to a separator curve whose existence is determined by the stable manifold of the equilibrium point m,0 that appears due to the depensation. This result implies that the exploited resource may become extinct when the biomass-effort ratio is small, consequently causing the fishery’s collapse. Using the most known of the functions to express depensation in the growth of the exploited species, we demonstrate the uniqueness of the limit cycle around the only positive equilibrium. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.