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Spreading Speed in an Integrodifference Predator–Prey System without Comparison Principle

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Abstract

In this paper, we study the spreading speed in an integrodifference system which models invasion of predators into the habitat of the prey. Without the requirement of comparison principle, we construct several auxiliary integrodifference equations and use the results of monotone scalar equations to estimate the spreading speed of the invading predators. We also present some numerical simulations to support our theoretical results and demonstrate that the integrodifference predator–prey system exhibits very complex dynamics. Our theory and numerical results imply that the invasion of predators may have a rough constant speed. Moreover, our numerical simulations indicate that the spatial contact of individuals and the overcompensatory phenomenon of the prey may be conducive to the persistence of nonmonotone biological systems and lead to instability of the predator-free state.

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Acknowledgements

We would like to thank the two anonymous reviewers for their very careful reading of the manuscript and very helpful comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Guo Lin & Yibin Niu

  2. School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, People’s Republic of China

    Shuxia Pan

  3. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Shigui Ruan

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  1. Guo Lin
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  2. Yibin Niu
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  3. Shuxia Pan
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  4. Shigui Ruan
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Correspondence to Shigui Ruan.

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G. Lin: Research was partially supported by NSF of China (Nos. 11731005, 11971213) and Fundamental Research Funds for the Central Universities (lzujbky-2020-11). S. Ruan: Research was partially supported by NSF (DMS-1853622)

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Lin, G., Niu, Y., Pan, S. et al. Spreading Speed in an Integrodifference Predator–Prey System without Comparison Principle. Bull Math Biol 82, 53 (2020). https://doi.org/10.1007/s11538-020-00725-y

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