Some remarks on traveling wave solutions in competition models

Bingtuan Li

doi:10.3934/dcdsb.2009.12.389

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2009, Volume 12, Issue 2: 389-399. Doi: 10.3934/dcdsb.2009.12.389

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Some remarks on traveling wave solutions in competition models

Bingtuan Li^1,

1.
Department of Mathematics, University of Louisville, Louisville, KY 40292

Received: November 30, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

We study the existence of traveling wave solutions for competition models in the form of integro-difference equations. We show that for a two-species competition model it is possible that two species spread at different speeds, and there exists a traveling wave solution. For an $m$-species competition model, under the assumption that species have the same dispersal and growth properties but have different competition abilities, we establish the existence of traveling wave solutions.

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Mathematics Subject Classification: Primary: 92D40, 92D25; Secondary: 47G10.

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