Nonautonomous Food-Limited Fishery Model With Adaptive Harvesting

TL;DR

This paper introduces a new food-limited fishery model with variable parameters, establishing criteria for positive periodic solutions and analyzing the impact of adaptive harvesting strategies through numerical simulations.

Contribution

It develops a novel food-limited fishery model with variable parameters and provides new criteria for the existence and stability of solutions, incorporating adaptive harvesting effects.

Findings

Existence of positive periodic solutions established.

Adaptive harvesting significantly influences fish stock stability.

Numerical simulations demonstrate parameter effects on fishery dynamics.

Abstract

We will introduce the biological motivation of the $\gamma$- food-limited model with variable parameters. New criteria are established for the existence and global stability of positive periodic solutions. To prove the existence of steady-state solutions, we used the upper-lower solution method where the existence of at least one positive periodic solution is obtained by constructing a pair of upper and lower solutions and application of the Friedreichs Theorem. Numerical simulations illustrate effects of periodic variation in the values of the basic biological and environmental parameters and how the adaptive harvesting strategies affect fishing stocks.