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A qualitative study on general Gause-type predator-prey models with constant diffusion rates. (English) Zbl 1144.35029
The authors study the solutions of a general Gause-type predator-prey model with constant diffusion rates under homogeneous Neumann boundary conditions. They investigate the existence and stability of constant homogeneous steady-state solutions. For certain parameter values they show the occurence of a Hopf bifurcation. Further they also investigate the existence conditions of spatially inhomogeneous solutions by using Leray-Schauder degree theory.

35K55Nonlinear parabolic equations
35B32Bifurcation (PDE)
35K57Reaction-diffusion equations
Full Text: DOI
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