American Institute of Mathematical Sciences

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2005, 2005(Special): 536-545. doi: 10.3934/proc.2005.2005.536

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

Kousuke Kuto 1, and  Yoshio Yamada 2,

1. 

Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
2. 

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

Received  September 2004 Revised  March 2005 Published  September 2005

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.
Keywords: cross-diffusion, Hopf bifurcation., stability, steady-state solution.
Mathematics Subject Classification: Primary: 35B32, 35J65; Secondary: 92D2.
Citation: Kousuke Kuto, Yoshio Yamada. Coexistence states for a prey-predator model with cross-diffusion. Conference Publications, 2005, 2005 (Special) : 536-545. doi: 10.3934/proc.2005.2005.536
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