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Stability analysis and bifurcations in a diffusive predator-prey system

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  • 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.
    Mathematics Subject Classification: Primary: 92D25 Secondary: 35K57, 35Q51, 35Q80.


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