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Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion

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Kuto K., Yamada Y.

Banach Center Publications

2004

tom 66

nr 1

199-210

This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give 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. Our method of analysis uses the idea developed by Du and Lou [6] and is based on the bifurcation theory and the Lyapunov-Schmidt reduction technique.

Ograniczanie wyników

1 Banach Center Publications

1 Kuto K.

1 Yamada Y.

1 2004

Wyniki wyszukiwania

Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion