Stability analysis and bifurcations in a diffusive predator-prey system
Leonid Braverman - Athabasca University, 1 University Drive, Athabasca, AB T9S 3A3, Canada (email)
Abstract: We consider a predator-prey system with logistic-type growth and linear diffusion for the prey, Holling type II functional response and the nonlinear diffusion $\nabla \left( \sigma n b \nabla b)$ for the predator, where $n$ is the prey (nutrient) and $b$ is the predator (bacteria) density, respectively. This corresponds to a collective-type behavior for predators: they spread faster when numerous enough at a front line. We present the complete linear stability analysis for this case, discuss some results of numerical simulations: the asymptotic behavior of the model (with the zero Neumann boundary conditions in a 2-D domain) was similar to the relevant Lotka-Volterra system of ordinary differential equations.
Keywords: Diffusive predator-prey system, nonlinear diffusion term, Holling type II
functional response, linear stability analysis, Hopf bifurcation
Received: July 2008; Revised: August 2009; Published: September 2009.