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Interactions leading to persistence in predator-prey systems with group defence

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Abstract

In previous work (Freedman and Wolkowicz, 1986;Bull. math. Biol. 48, 493–508) it was shown that in a predator-prey system where the prey population exhibits group defence, it is possible that enrichment of the environment could lead to extinction of the predator population.

In this paper a third population is introduced and criteria are derived under which persistence of all populations will occur. In particular, criteria for a superpredator and for a competitor to stabilize the system in the sense of persistence are analyzed.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    H. I. Freedman

  2. Department of Mathematics and Mechanics, Lanzhou University, Lanzhou, Gansu, People's Republic of China

    Quan Hongshun

Authors
  1. H. I. Freedman
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  2. Quan Hongshun
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Additional information

Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823.

This research was carried out while the author was a visiting scholar at the University of Alberta.

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Freedman, H.I., Hongshun, Q. Interactions leading to persistence in predator-prey systems with group defence. Bltn Mathcal Biology 50, 517–530 (1988). https://doi.org/10.1007/BF02458850

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  • DOI: https://doi.org/10.1007/BF02458850

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