title: Persistence in reaction diffusion models with weak allee effect.
abstract: 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.
authors.affiliation: Department of Mathematics, College of William and Mary, Williamsburg, VA 23185, USA. shij@math.wm.edu
authors.forename: Junping
authors.initials: J
authors.lastname: Shi
authors.forename: Ratnasingham
authors.initials: R
authors.lastname: Shivaji
mesh_terms: D000818:Animals; D004777:Environment; D008954:Models, Biological; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics