Isaac Scientific Publishing

Advances in Analysis

An Optimal Control Problem for a Predator-prey Model with a General Monotonic or Non-monotonic Functional Response for Prey

Download PDF (441.4 KB) PP. 227 - 231 Pub. Date: October 20, 2017

DOI: 10.22606/aan.2017.24001

Author(s)

  • Wensheng Yang*
    School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, P. R. China
    Fujian Key Laborotary of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, P. R.

Abstract

An optimal control problem is studied for a predator-prey model with a general monotonic and non-monotonic functional response for prey. The control functions represent the rate of mixture of the populations and the cost functional is of Mayer type. The goal of this paper is to maximize the total density of the two populations at a fixed time moment. The number of switching points of the optimal control is determined by the threshold value c, which is the rate of translating the prey population into the predator population. It is shown that general monotonic or non-monotonic functional response has no influence on the number of switching points of the optimal control.

Keywords

Predator-prey model, general functional response, Pontryagin’s maximum principle, bang-bang control, switching point.

References

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