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