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

Pages: 536 - 545, Issue Special, August 2005

 Abstract        Full Text (229.9K)              

Kousuke Kuto - Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan (email)
Yoshio Yamada - Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku 169-8555, Tokyo, Japan (email)

Abstract: 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, steady-state solution, stability, Hopf bifurcation.
Mathematics Subject Classification:  Primary: 35B32, 35J65; Secondary: 92D25.

Received: September 2004;      Revised: March 2005;      Published: September 2005.