Nonlinear Dynamics

, Volume 67, Issue 4, pp 2543–2548 | Cite as

Remarks on cannibalism and pattern formation in spatially extended prey–predator systems

Original Paper

Abstract

The relationships between cannibalism and pattern formation in spatially extended prey–predator systems are studied with a model that degenerates, in the absence of cannibalism, into the most standard prey–predator model, known as Rosenzweig–MacArthur model. The analysis is based on the theory developed long ago by Turing in his famous paper on morphogenesis, but in a special form, which allows one to decouple the role of demographic parameters from that of diffusive dispersal. The proofs are given in terms of prey and predator nullclines because ecologists are mainly familiar with this technique. The final result of the analysis is that spatial pattern can exist only in systems with highly cannibalistic and highly dispersing predator provided the attractor of the system in the absence of cannibalism is a limit cycle. This result is more simple and more complete than that published in this journal a few years ago by Sun and coauthors.

Keywords

Prey–predator models Spatial pattern Turing instability Cannibalism Dispersal 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.DEIPolitecnico di MilanoMilanoItaly
  2. 2.Evolution and Ecology ProgramInternational Institute for Applied Systems AnalysisLaxenburgAustria

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