A pulse fishery model with closures as function of the catch: Conditions for sustainability

TL;DR

This paper introduces a novel pulse fishery model using impulsive differential equations where closure durations depend on previous catch, identifying effort thresholds for sustainability or extinction.

Contribution

It develops a new impulsive differential equation model for pulse fisheries with catch-dependent closures, providing conditions for sustainability.

Findings

Identifies a fishing effort threshold for sustainability.

Demonstrates conditions leading to fishery extinction.

Provides a mathematical framework for pulse fishery management.

Abstract

We present a model of single species fishery which alternates closed seasons with pulse captures. The novelty is that the length of a closed season is determined by the stock size of the last capture. The process is described by a new type of impulsive differential equations recently introduced. The main result is a fishing effort threshold which determines either the sustainability of the fishery or the extinction of the resource.