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Journal of Optimization
Volume 2019, Article ID 9512879, 12 pages
https://doi.org/10.1155/2019/9512879
Research Article

Theoretical Analysis of an Imprecise Prey-Predator Model with Harvesting and Optimal Control

Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal-721101, India

Correspondence should be addressed to Anjana Das; moc.liamg@ajna.8891

Received 16 May 2018; Accepted 10 December 2018; Published 21 January 2019

Academic Editor: K. F. C. Yiu

Copyright © 2019 Anjana Das and M. Pal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In our present paper, we formulate and study a prey-predator system with imprecise values for the parameters. We also consider harvesting for both the prey and predator species. Then we describe the complex dynamics of the proposed model system including positivity and uniform boundedness of the system, and existence and stability criteria of various equilibrium points. Also the existence of bionomic equilibrium and optimal harvesting policy are thoroughly investigated. Some numerical simulations have been presented in support of theoretical works. Further the requirement of considering imprecise values for the set of model parameters is also highlighted.