Dynamical complexity induced by Allee effect in a predator–prey model

In this paper, we investigate the complex dynamics induced by Allee effect in a predator–prey model. For the non-spatial model, Allee effect remains the boundedness of positive solutions, and it also induces the model to exhibit one or two positive equilibria. Especially, in the case with strong All...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 16; pp. 103 - 119
Main Authors Wang, Weiming, Zhu, Ya-nuo, Cai, Yongli, Wang, Wenjuan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2014
Subjects
Diffusion
Diffusion effects
Dynamic tests
Dynamics
Instability
Mathematical models
Replication
Stability
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ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2013.09.010

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Summary:In this paper, we investigate the complex dynamics induced by Allee effect in a predator–prey model. For the non-spatial model, Allee effect remains the boundedness of positive solutions, and it also induces the model to exhibit one or two positive equilibria. Especially, in the case with strong Allee effect, the model is bistable. For the spatial model, without Allee effect, there is the nonexistence of diffusion-driven instability. And in the case with Allee effect, the positive equilibrium can be unstable under certain conditions. This instability is induced by Allee effect and diffusion together. Furthermore, via numerical simulations, the model dynamics exhibits both Allee effect and diffusion controlled pattern formation growth to holes, stripe–hole mixtures, stripes, stripe–spot mixtures, and spots replication. That is to say, the dynamics of the model with Allee effect is not simple, but rich and complex.
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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2013.09.010