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Traveling wave solutions of a nonlocal dispersal predator–prey model with spatiotemporal delay

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Abstract

In this paper, we study the existence and nonexistence of traveling wave solution for the nonlocal dispersal predator–prey model with spatiotemporal delay. This model incorporates the Leslie–Gower functional response into the Lotka–Volterra-type system, and both species obey the logistic growth. We explore the existence of traveling wave solution for \(c\ge c^{\star }\) by using the upper-lower solutions and the Schauder’s fixed point theorem. Furthermore, the nonexistence of traveling wave solution for \(c<c^{\star }\) is discussed by means of the comparison principle. The novelty of this work lies in the construction of upper-lower solutions and the proof of the complete continuity of operator.

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Acknowledgements

The first author would like to thank the School of Mathematical and Statistical Sciences of University of Texas Rio Grande Valley for its hospitality and generous support during his visiting from September 2017 to September 2018.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology, Beijing, Beijing, 100083, China

    Zhihong Zhao, Rui Li & Xiangkui Zhao

  2. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA

    Zhaosheng Feng

Authors
  1. Zhihong Zhao
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  2. Rui Li
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  3. Xiangkui Zhao
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  4. Zhaosheng Feng
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Corresponding authors

Correspondence to Zhihong Zhao or Zhaosheng Feng.

Additional information

This work is supported by National Science Foundation of China under 11601029 and China Scholarship Council Award.

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Zhao, Z., Li, R., Zhao, X. et al. Traveling wave solutions of a nonlocal dispersal predator–prey model with spatiotemporal delay. Z. Angew. Math. Phys. 69, 146 (2018). https://doi.org/10.1007/s00033-018-1041-7

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  • DOI: https://doi.org/10.1007/s00033-018-1041-7

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