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Coexistence states for a prey-predator model with cross-diffusion

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  • This paper discusses a prey-predator system with cross-diffusion. We can prove that the set of coexistence steady-states of this system contains an S or $\supset$-shaped branch with respect to a bifurcation parameter in a large cross-diffusion case. We give also some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case.
    Mathematics Subject Classification: Primary: 35B32, 35J65; Secondary: 92D25.

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