Optimal harvesting in predator-prey systems

Fred Brauer; A. C. Soudack

doi:10.1080/0020718508961113

Optimal harvesting in predator-prey systems

Fred Brauer, A. C. Soudack

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the harvesting of predators in a predator-prey system as an optimal control problem with the goal of maximizing the long-term average yield. We show that the maximum yield can not be greater than the largest constant-rate harvest for which the system has an equilibrium, provided the controlled system tends to an equilibrium or has a periodic solution. We also give some examples indicating practical strategies using either bang-bang or instantaneous harvests whose yields approach this maximum.

Original language	English (US)
Pages (from-to)	111-128
Number of pages	18
Journal	International Journal of Control
Volume	41
Issue number	1
DOIs	https://doi.org/10.1080/0020718508961113
State	Published - Jan 1985
Externally published	Yes

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications

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10.1080/0020718508961113

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title = "Optimal harvesting in predator-prey systems",

abstract = "We study the harvesting of predators in a predator-prey system as an optimal control problem with the goal of maximizing the long-term average yield. We show that the maximum yield can not be greater than the largest constant-rate harvest for which the system has an equilibrium, provided the controlled system tends to an equilibrium or has a periodic solution. We also give some examples indicating practical strategies using either bang-bang or instantaneous harvests whose yields approach this maximum.",

author = "Fred Brauer and Soudack, {A. C.}",

note = "Funding Information: t Department of Mathematics, University or Wisconsin, Madison, Wisconsin 53706, U.S.A. $ Department of Electrical Engineering, University of British Columbia, Vancouver, British Columbia V6T 1W 5, Canada. 5 Visiting Professor, Weizrnann Institute of Science, Rehovot, Israel; research supported in part by NSERC grant 67-3 138.",

year = "1985",

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PY - 1985/1

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N2 - We study the harvesting of predators in a predator-prey system as an optimal control problem with the goal of maximizing the long-term average yield. We show that the maximum yield can not be greater than the largest constant-rate harvest for which the system has an equilibrium, provided the controlled system tends to an equilibrium or has a periodic solution. We also give some examples indicating practical strategies using either bang-bang or instantaneous harvests whose yields approach this maximum.

AB - We study the harvesting of predators in a predator-prey system as an optimal control problem with the goal of maximizing the long-term average yield. We show that the maximum yield can not be greater than the largest constant-rate harvest for which the system has an equilibrium, provided the controlled system tends to an equilibrium or has a periodic solution. We also give some examples indicating practical strategies using either bang-bang or instantaneous harvests whose yields approach this maximum.

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Optimal harvesting in predator-prey systems

Abstract

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