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This chapter focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur predator-prey model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic wave train solution in the large wave speed asymptotic. Depending on the model parameters we more particularly study the existence and uniqueness of a traveling wave connecting two equilibria or connecting an equilibrium point and a periodic wave train.

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Large Speed Traveling Waves for the Rosenzweig-MacArthur predator-prey Model with Spatial Diffusion

  • 章节

  • 发表日期：

    2026年

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  • Arnaud Ducrot,
  • Quentin Griette,
  • Zhihua Liu,
  • Pierre Magal

摘要

This chapter focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur predator-prey model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic wave train solution in the large wave speed asymptotic. Depending on the model parameters we more particularly study the existence and uniqueness of a traveling wave connecting two equilibria or connecting an equilibrium point and a periodic wave train.