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Attraction–repulsion taxis mechanisms in a predator–prey model

Author

Listed:
  • Jonathan Bell

    (University of Maryland Baltimore County)

  • Evan C. Haskell

    (Nova Southeastern University)

Abstract

We consider a predator–prey model where the predator population favors the prey through biased diffusion toward the prey density, while the prey population employs a chemical repulsive mechanism. This leads to a quasilinear parabolic system. We first establish the global existence of positive solutions. Thereafter we show the existence of nontrivial steady state solutions via bifurcation theory, then we discuss the stability of these branch solutions. Through numerical simulation we analyze the nature of patterns formed and interpret results in terms of the survival and distribution of the two populations.

Suggested Citation

  • Jonathan Bell & Evan C. Haskell, 2021. "Attraction–repulsion taxis mechanisms in a predator–prey model," Partial Differential Equations and Applications, Springer, vol. 2(3), pages 1-29, June.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:3:d:10.1007_s42985-021-00080-0
    DOI: 10.1007/s42985-021-00080-0
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    References listed on IDEAS

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    1. Liu, Xia & Zhang, Tonghua & Meng, Xinzhu & Zhang, Tongqian, 2018. "Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 446-460.
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    Cited by:

    1. Haskell, Evan C. & Bell, Jonathan, 2021. "A model of the burglar alarm hypothesis of prey alarm calls," Theoretical Population Biology, Elsevier, vol. 141(C), pages 1-13.

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