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Traveling Wave Solutions for Some Classes of Diffusive Predator–Prey Models

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Abstract

We investigate the traveling wave solutions for some types of diffusive Predator–prey systems, including the models with prey and predator dependent functional response, that have served as models to study the dynamics of Predator–prey interaction. The method used to show the existence of traveling waves and to identify minimum wave speed consists of two steps. First we obtain globally defined solutions by a shooting argument that is a modification of a recently developed method. We then show the convergence of these global solutions to an interior equilibrium point by the construction of a Liapunov function.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Wei Ding & Wenzhang Huang

  2. Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Wenzhang Huang

Authors
  1. Wei Ding
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  2. Wenzhang Huang
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Correspondence to Wenzhang Huang.

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Ding, W., Huang, W. Traveling Wave Solutions for Some Classes of Diffusive Predator–Prey Models. J Dyn Diff Equat 28, 1293–1308 (2016). https://doi.org/10.1007/s10884-015-9472-8

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  • DOI: https://doi.org/10.1007/s10884-015-9472-8

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