About reaction–diffusion systems involving the Holling-type II and the Beddington–DeAngelis functional responses for predator–prey models

We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching predators, and show that its solutions converge when a small parameter tends to 0 towards the solutions of a reaction–cross diffusion system of...

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Bibliographic Details
Published in:Nonlinear differential equations and applications 2018-06, Vol.25 (3), Article 24
Main Authors: Conforto, F., Desvillettes, Laurent, Soresina, C.
Format: Article
Language:English
Subjects:
Analysis
Diffusion
Mathematical models
Mathematics
Mathematics and Statistics
Predator-prey simulation
Stability
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Summary:We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching predators, and show that its solutions converge when a small parameter tends to 0 towards the solutions of a reaction–cross diffusion system of predator–prey type involving a Holling-type II or Beddington–DeAngelis functional response. We also provide a study of the Turing instability domain of the obtained equations and (in the case of the Beddington–DeAngelis functional response) compare it to the same instability domain when the cross diffusion is replaced by a standard diffusion.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-018-0515-9