Journal of Mathematical Biology

, Volume 52, Issue 6, pp 807–829 | Cite as

Persistence in reaction diffusion models with weak allee effect



We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak Allee effect type growth, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a heterogeneous bounded region. The existence of multiple steady states is shown, and the global bifurcation diagrams are obtained. Results are applied to a reaction-diffusion model with type II functional response, and also a model with density-dependent diffusion of animal aggregation.

Mathematics Subject Classification (2000)

35J65 35B32 92D25 92D40 35Q80 

Key words or phrases

Population biology Reaction-diffusion equation Allee effect Global Bifurcation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsCollege of William and MaryWilliamsburgUSA
  2. 2.School of MathematicsHarbin Normal UniversityHarbinP.R.China
  3. 3.Department of MathematicsMississippi State UniversityMississippi StateUSA

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