Traveling Wave Solution of a Reaction–Diffusion Predator–Prey System

  • Jiang Liu
  • Dongcheng Xu
  • Zengji Du


In this paper, we discuss a reaction–diffusion predator–prey model with nonlocal delays. By using the theory of dynamical systems, specifically based on geometric singular perturbation theory, center manifold theorem and Fredholm theory, we construct an invariant manifold for the associated predator–prey equation and use this invariant manifold to obtain a heteroclinic orbit between two non-negative equilibrium points. Furthermore, we establish the existence result of traveling wave solution for the predator–prey model.


Predator–prey model Traveling wave Geometric singular perturbation Nonlocal delays 

Mathematics Subject Classification

35K57 34D15 92D25 



The authors express their sincere thanks to the anonymous reviewers for their valuable comments and careful corrections for improving the quality of the paper.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouPeople’s Republic of China

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