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Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking. (English) Zbl 1176.92050
Summary: The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. We examine the strategies of using stocking and harvesting to prevent the extinction of the weak species in a competitive exclusion environment. We find that in a system governed by the P. H. Leslie and J. C. Gower model [Biometrika 47, 219–234 (1960; Zbl 0103.12502)] careful stocking will ensure the coexistence between all species. We also find that constant harvesting of the dominant species may guarantee the survival of the weaker species when the parameters of the model are in a certain range. Mixed strategies and conditional harvesting strategies are also discussed.

MSC:
92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
39A60 Applications of difference equations
39A30 Stability theory for difference equations
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