A two-patch prey-predator model with predator dispersal driven by the predation strength

Yun Kang, Sourav Kumar Sasmal, Komi Messan

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Foraging movements of predator play an important role in pop- ulation dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide com- pleted local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabi- lize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.

Original languageEnglish (US)
Pages (from-to)843-880
Number of pages38
JournalMathematical Biosciences and Engineering
Volume14
Issue number4
DOIs
StatePublished - Aug 1 2017

Keywords

  • Dispersal
  • Non-random foraging movements
  • Persistence
  • Rosenzweig-MacArthur prey-predator model
  • Self-organization effects

ASJC Scopus subject areas

  • Medicine(all)
  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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