title: Simple finite element methods for approximating predator-prey dynamics in two dimensions using MATLAB.
abstract: We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area.
authors.affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada, mgarvie@uoguelph.ca.
authors.forename: Marcus R
authors.initials: MR
authors.lastname: Garvie
authors.forename: John
authors.initials: J
authors.lastname: Burkardt
authors.forename: Jeff
authors.initials: J
authors.lastname: Morgan
mesh_terms: D000818:Animals; D017753:Ecosystem; D020342:Finite Element Analysis; D020387:Food Chain; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D012984:Software