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Positive steady states for a prey-predator cross-diffusion system with a protection zone and Holling type II functional response

Pages: 597 - 603, Issue special, November 2013

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Kazuhiro Oeda - Department of Applied Mathematics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan (email)

Abstract: This paper is concerned with the steady state problem of a prey-predator cross-diffusion system with a protection zone and Holling type II functional response. A sufficient condition for the existence of positive steady state solutions is given. Our proof is based on the bifurcation theory and some a priori estimates.

Keywords:  Prey-predator model, protection zone, cross-diffusion, coexistence states, functional response.
Mathematics Subject Classification:  Primary: 35B32, 35J57; Secondary: 92D25.

Received: September 2012;      Revised: March 2013;      Published: November 2013.

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