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Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey

Author

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  • Malay Banerjee

    (Department of Mathematics and Statistics, IIT Kanpur, Kanpur 208016, India
    These authors contributed equally to this work.)

  • Nayana Mukherjee

    (Department of Mathematics and Statistics, IIT Kanpur, Kanpur 208016, India
    These authors contributed equally to this work.)

  • Vitaly Volpert

    (Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
    These authors contributed equally to this work.)

Abstract

Spatiotemporal pattern formation in integro-differential equation models of interacting populations is an active area of research, which has emerged through the introduction of nonlocal intra- and inter-specific interactions. Stationary patterns are reported for nonlocal interactions in prey and predator populations for models with prey-dependent functional response, specialist predator and linear intrinsic death rate for predator species. The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators. We derive the conditions of the Turing and of the spatial Hopf bifurcation around the coexisting homogeneous steady-state and verify the analytical results through extensive numerical simulations. Bifurcations of spatial patterns are also explored numerically.

Suggested Citation

  • Malay Banerjee & Nayana Mukherjee & Vitaly Volpert, 2018. "Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey," Mathematics, MDPI, vol. 6(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:3:p:41-:d:135394
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    References listed on IDEAS

    as
    1. Jef Huisman & Franz J. Weissing, 1999. "Biodiversity of plankton by species oscillations and chaos," Nature, Nature, vol. 402(6760), pages 407-410, November.
    2. Fasani, Stefano & Rinaldi, Sergio, 2011. "Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems," Ecological Modelling, Elsevier, vol. 222(18), pages 3449-3452.
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