Traveling waves for the Lotka-Volterra predator-prey system without diffusion of the predator

Yuzo Hosono

doi:10.3934/dcdsb.2015.20.161

Article Contents

2015, Volume 20, Issue 1: 161-171. Doi: 10.3934/dcdsb.2015.20.161

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Traveling waves for the Lotka-Volterra predator-prey system without diffusion of the predator

Yuzo Hosono^1,

1.
Department of Mathematics, Kyoto Sangyo University, Kyoto 603

Received: October 31, 2013

Revised: June 30, 2014

Published: December 2014

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Abstract

This paper investigates the existence of traveling waves and their propagation speeds for the Lotka-Volterra predator-prey reaction-diffusion models with no predator diffusion. We prove the existence of traveling waves with any positive speed. Our mathematical tool is the shooting argument in the phase space based on the Wazewski theorem.

Keywords:

Traveling waves,
propagation speed,
the Lotka-Volterra predator-prey system,
the Wazewski theorem.

Mathematics Subject Classification: Primary: 35C07, 35K57; Secondary: 92D25.

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