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

Yongli Cai, Malay Banerjee, Yun Kang, Weiming Wang

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume11
Issue number6
DOIs
StatePublished - Dec 1 2014

Fingerprint

Allee Effect
Predator-prey Model
predators
Mortality
Turing Instability
Growth
Predator
Controlled Diffusions
Model
Hopf bifurcation
Functional Response
Dependent
Predator-prey System
functional response models
Prey
Hopf Bifurcation
Persistence
Replication
Nonexistence
Positive Solution

Keywords

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

ASJC Scopus subject areas

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

Cite this

Spatiotemporal complexity in a predator-prey model with weak allee effects. / Cai, Yongli; Banerjee, Malay; Kang, Yun; Wang, Weiming.

In: Mathematical Biosciences and Engineering, Vol. 11, No. 6, 01.12.2014, p. 1247-1274.

Research output: Contribution to journalArticle

Cai, Yongli ; Banerjee, Malay ; Kang, Yun ; Wang, Weiming. / Spatiotemporal complexity in a predator-prey model with weak allee effects. In: Mathematical Biosciences and Engineering. 2014 ; Vol. 11, No. 6. pp. 1247-1274.
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