Response of predator-prey systems to nutrient enrichment and proportional harvesting

F. Brauer; A. C. Soudack

doi:10.1080/00207177808922348

Response of predator-prey systems to nutrient enrichment and proportional harvesting

F. Brauer, A. C. Soudack

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

16 Scopus citations

Abstract

A predator-prey System is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting at a rate proportional to the predator population size are studied. Some theoretical analysis concerning the stability of equilibrium points and the existence of stable limit cycles are included. Three models are examined as examples, and for two of them computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and increase of harvesting effort. The essential difference between this study and our previous work on constant-rate harvesting (Brauer et al. 1976) is that, here, extinction of predators in finite time is impossible although the predator population may tend to zero as l→∞.

Original language	English (US)
Pages (from-to)	65-86
Number of pages	22
Journal	International Journal of Control
Volume	27
Issue number	1
DOIs	https://doi.org/10.1080/00207177808922348
State	Published - Jan 1978
Externally published	Yes

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications

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title = "Response of predator-prey systems to nutrient enrichment and proportional harvesting",

abstract = "A predator-prey System is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting at a rate proportional to the predator population size are studied. Some theoretical analysis concerning the stability of equilibrium points and the existence of stable limit cycles are included. Three models are examined as examples, and for two of them computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and increase of harvesting effort. The essential difference between this study and our previous work on constant-rate harvesting (Brauer et al. 1976) is that, here, extinction of predators in finite time is impossible although the predator population may tend to zero as l→∞.",

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

note = "Funding Information: Received 30 July 1976. t Department of Mathematics, University of Wisconsin, Madison, U.S.A. t Department of Electrical Engineering, University of British Columbia, Vancouver, Canada. Research sponsored in part by the United States Army under Contract No. DAAG29-75-C-0024 and in part by the National Research Council of Canada, Grant No. 67-3138. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.",

year = "1978",

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doi = "10.1080/00207177808922348",

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N2 - A predator-prey System is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting at a rate proportional to the predator population size are studied. Some theoretical analysis concerning the stability of equilibrium points and the existence of stable limit cycles are included. Three models are examined as examples, and for two of them computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and increase of harvesting effort. The essential difference between this study and our previous work on constant-rate harvesting (Brauer et al. 1976) is that, here, extinction of predators in finite time is impossible although the predator population may tend to zero as l→∞.

AB - A predator-prey System is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting at a rate proportional to the predator population size are studied. Some theoretical analysis concerning the stability of equilibrium points and the existence of stable limit cycles are included. Three models are examined as examples, and for two of them computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and increase of harvesting effort. The essential difference between this study and our previous work on constant-rate harvesting (Brauer et al. 1976) is that, here, extinction of predators in finite time is impossible although the predator population may tend to zero as l→∞.

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Response of predator-prey systems to nutrient enrichment and proportional harvesting

Abstract

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