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. J. S. is partially supported by United States NSF grants DMS-0314736 and EF-0436318, College of William and Mary summer grants, and a grant from Science Council of Heilongjiang Province, China.