Elsevier

Journal of Theoretical Biology

Volume 75, Issue 3, 7 December 1978, Pages 249-262
Journal of Theoretical Biology

On a diffusive prey-predator model which exhibits patchiness

https://doi.org/10.1016/0022-5193(78)90332-6Get rights and content

Abstract

Spatial heterogeneity (patchiness) in certain predator-prey situations has been observed even though their environment appears homogeneous. As a model mechanism to explain this patchiness phenomenon we propose a predator-prey interaction system with diffusive effects. We show that when the diffusion of the prey is small compared with that of the predator the non-linearity which we call a hump effect in the prey interaction, is a key mechanism for the system to exhibit, asymptotically in time, stable heterogeneity in a bounded domain with zero flux boundary conditions. The model can reasonably be applied to certain terrestrial plant-herbivore systems.

References (18)

  • P.C. Fife

    J. Chem. Phys

    (1976)
  • S.A. Levin et al.

    Nature

    (1976)
  • J.D. Murray
  • J.H. Steele

    Nature

    (1974)
  • R.M. Cassie

    Oceanogr. Mar. Biol. Ann. Reg

    (1963)
  • E.D. Conway et al.

    SIAM J. Appl. Maths

    (1978)
    Conway, E. D. & Smoller, J. A. (1977)....
  • D.M. Dubois

    Ecol. Mod

    (1975)
  • P.C. Fife

    J. Math. Anal. Appl

    (1976)
  • R.M. May
There are more references available in the full text version of this article.

Cited by (160)

  • Parameter estimation for network-organized Turing system based on convolution neural networks

    2024, Communications in Nonlinear Science and Numerical Simulation
  • Non-reciprocal interactions enhance heterogeneity

    2022, Chaos, Solitons and Fractals
View all citing articles on Scopus
View full text