Persistence in reaction diffusion models with weak allee effect

• DOI: 10.1007/s00285-006-0373-7
• Publication Date: 2006-03-06T14:22:15Z
• Authors: Junping Shi; Ratnasingham Shivaji
• Keywords: Population Density; Models, Statistical; Population Dynamics; 0103 physical sciences; Animals; Environment; Models, Biological; 01 natural sciences

We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak allele 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.