Properties of Traveling Wave Fronts for Three Species Lotka–Volterra System

Abstract

The purpose of this paper is to investigate properties of traveling wave fronts for three species Lotka–Volterra system: the asymptotic behavior and uniqueness. Applying the Ikehara’s theorem, we determine the exponential rates of traveling wave fronts at the negative infinity. We further investigate the uniqueness of traveling wave fronts with the help of the sliding method.

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Acknowledgements

The research of Weiguo Zhang was partially supported by National Natural Science Foundation of China (No. 11471215), by Shanghai Leading Academic Discipline Project (No. XTKX2012) and by the Hujiang Foundation of China (B14005). Yanling Meng is supported by Natural Science Foundation of Shanghai (No.18ZR1426500). The authors would like to thank the anonymous referees for their valuable comments and suggestions which have led to an improvement of the presentation.

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Meng, Y., Zhang, W. Properties of Traveling Wave Fronts for Three Species Lotka–Volterra System. Qual. Theory Dyn. Syst. 19, 67 (2020). https://doi.org/10.1007/s12346-020-00404-2

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Keywords

  • Traveling wave fronts
  • Competitive-cooperative Lotka–Volterra system
  • Asymptotic behavior
  • Uniqueness
  • The sliding method

Mathematics Subject Classification

  • 35C07
  • 92D25
  • 35B35