Spatiotemporal complexity in a predator-prey model with weak allee effects

Yongli Cai, Malay Banerjee, Yun Kang, Weiming Wang

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


In this article, we study the rich dynamics of a diffusive predatorprey system with Allee effects in the prey growth. Our model assumes a preydependent Holling type-II functional response and a density dependent death rate for predator. We investigate the dissipation and persistence property, the stability of nonnegative and positive constant steady state of the model, as well as the existence of Hopf bifurcation at the positive constant solution. In addition, we provide results on the existence and non-existence of positive nonconstant solutions of the model. We also demonstrate the Turing instability under some conditions, and find that our model exhibits a diffusion-controlled formation growth of spots, stripes, and holes pattern replication via numerical simulations. One of the most interesting findings is that Turing instability in the model is induced by the density dependent death rate in predator.

Original languageEnglish (US)
Pages (from-to)1247-1274
Number of pages28
JournalMathematical Biosciences and Engineering
Issue number6
StatePublished - Dec 1 2014


  • Allee effects
  • Density dependent
  • Non-constant solution
  • Pattern formation
  • Turing instability

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics


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