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

• Autorzy: Kousuke Kuto , Yoshio Yamada
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35J65: Nonlinear boundary value problems for linear elliptic equations
• 92D25: Population dynamics (general)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 66
• Numer: 1
• Strony: 199-210

Daty

wydano

2004

Twórcy

autor

Kousuke Kuto

• Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

autor

Yoshio Yamada

• Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Identyfikatory

DOI

10.4064/bc66-0-13