Electron. J. Diff. Equ., Vol. 2012 (2012), No. 197, pp. 1-13.

Traveling waves in a diffusive predator-prey model with general functional response

Zhaoquan Xu, Peixuan Weng

Abstract:
This article concerns the existence of traveling waves in a diffusive predator-prey model with general functional response. By applying the Schauder fixed theorem, we establish existence results of traveling wave solutions. The results are then applied to the predator-prey model with Holling type-II response. Our results indicate that there is a transition zone moving from the state with no species to the coexistence state of both species.

Submitted February 20, 2012. Published November 10, 2012.
Math Subject Classifications: 34C12, 34C37, 35K57, 92D25.
Key Words: Traveling waves; general functional response; Schauder's fixed theorem.

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Peixuan Weng
School of Mathematics, South China Normal University
Guangzhou 510631, China
email: wengpx@scnu.edu.cn, Tel: 0086-20-85213533
Zhaoquan Xu
School of Mathematics, South China Normal University
Guangzhou 510631, China
email: xiaozhao20042008@163.com

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