@article{2b161d69003e40c0b76b2f7616375bbc,
title = "Stabilization and de-stabilization of predator-prey systems under harvesting and nutrient enrichment",
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 on the stability of the system are studied. Some theoretical analysis concerning the existence of equilibrium points and limit cycles is included. Three models are examined as examples and the concept of practical stability is introduced. For one of the models, computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and harvesting. The results indicate that care must be taken in harvesting to prevent extinction of the predator and a resulting collapse of the entire ecosystem. This study should, therefore, prove to be a useful tool in resource management and control.",
author = "F. Brauer and Soudack, {A. C.} and Jarosch, {H. S.}",
note = "Funding Information: In many practical situations the predator may be harvested and removed from the system. This could occur, for example, if the predator is being used as a food supply for a third species. Another problem of this nature involves lake phytoplankton as predator and nutrient as prey. Observations indicate that there are oscillations of large amplitude, and it would be of interest if these oscillations could be tamed by judicious harvesting of phytoplankton. For these reasons we are interested in studying the effect of Received 9 July 1975. t The Weizmann Institute of Science, Rehovot, Israel. t On leave from Department of Mathematics, University of Wisconsin, Madison, Wisconsin, U.S.A. Research supported in part by Wisconsin Alumni Research Foundation. § On leave from Department of Electrical Engineering, University of British Columbia, Vancouver, Canada. II Computing Centre, Weizman Institute of Science. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",
year = "1976",
month = apr,
doi = "10.1080/00207177608922181",
language = "English (US)",
volume = "23",
pages = "553--573",
journal = "International Journal of Control",
issn = "0020-7179",
publisher = "Taylor and Francis Ltd.",
number = "4",
}