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Permanence and Stability of a Kill the Winner Model in Marine Ecology

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Abstract

We focus on the long-term dynamics of “killing the winner” Lotka–Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.

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Acknowledgements

The authors would like to thank the anonymous reviewer for their valuable comments and suggestions to improve the quality of the paper. This work was supported by a Grant from the Simons Foundation (355819, H.L.S.).

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Daniel A. Korytowski & Hal Smith

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  1. Daniel A. Korytowski
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  2. Hal Smith
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Correspondence to Daniel A. Korytowski.

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Korytowski, D.A., Smith, H. Permanence and Stability of a Kill the Winner Model in Marine Ecology. Bull Math Biol 79, 995–1004 (2017). https://doi.org/10.1007/s11538-017-0265-6

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  • DOI: https://doi.org/10.1007/s11538-017-0265-6

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