Existence and optimal harvesting of two competing species in a polluted environment with pollution reduction effect

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Natural and Computational Sciences, Arba Minch University, Ethiopia

2 Sri Sathya Sai University for Human Excellence, Gulbarga, India

Abstract

This paper deals with the existence and optimal harvesting of two competing species in a polluted environment under the influence of pollution reduction effort. We propose and analyze a nonlinear system wherein harvesting and pollution reduction activities, respectively, are incorporated into the resource and pollution dynamic equations. We investigate the coexistence, competitive exclusion, and extinction of both species in the system. Further, considering pollution-dependent revenues, we study an optimal harvest problem on an infinite horizon. The results indicate that the extinction of both species is inevitable when pollutant inflow is sufficiently large.  Otherwise, the proper effort allocation towards pollution reduction guarantees not only species coexistence but also improves the revenue. The significant outcomes of the study are verified by considering practical examples.

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