Time Delays and Pollution in an Open Access Fishery

Abstract

We analyze the impacts of pollution on fishery sectorusing a dynamical system approach. The proposedmodel presupposes that the economic developmentcauses emissions that either remediate or accumulatein the oceans. The model possesses a block structurewhere the solutions of the rate equations for thepollutant and the economic activity act as an input forthe biomass and effort equation. We also account fordistributed delay effects in both the pollution level andthe economic activity level in our modeling framework.The weight functions in the delay terms are expressedin terms of exponentially decaying functions, which inturn enable us to convert the modeling framework to ahigher‐order autonomous dynamical system by meansof a linear chain trick. When both the typical delaytime for the economic activity and the typical delaytime for the pollution level are much smaller than thebiomass time scale, the governing system is analyzedby means of the theory for singularly perturbeddynamical systems. Contrary to what is found forpopulation dynamical systems with absolute delays, wereadily find that the impact of the distributed time lags is negligible in the long‐run dynamics in this time‐scaleseparation regime.