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Properties of traveling waves in an impulsive reaction–diffusion model with overcompensation

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Abstract

The phenomenon of overcompensation is widespread in ecology, and non-monotonic discrete-time map may admit complex dynamics. This paper focuses on the impact of overcompensation on the propagation of a spatially moving population with a birth pulse. We prove the upward convergence of the oscillating traveling wave when the birth function is a unimodal function. We establish the existence of monotone and non-monotone traveling wave solutions for the second iterative operator. Furthermore, we obtain the existence, uniqueness, and stability of the standing wave solutions for the second iterative operator. Numerical simulations are performed to illustrate and complement the theoretical results.

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Acknowledgements

Z Wang’s research was partially supported by the Project funded by China Postdoctoral Science Foundation (No. 2022M723058) and Fundamental Research Funds for the Central Universities. Q An’s research was partially supported by Natural Science Found of Jiangsu province BK20200805 and Natural Science Fund Project of Colleges in Jiangsu Province 20KJB110009. H Wang’s research was partially supported by NSERC Discovery Grant RGPIN-2020-03911 and NSERC Accelerator Grant RGPAS-2020-00090. The authors are very grateful to the anonymous referee for careful reading and many valuable comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Zhenkun Wang

  2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Qi An

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Hao Wang

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  1. Zhenkun Wang
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  2. Qi An
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  3. Hao Wang
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Correspondence to Hao Wang.

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Wang, Z., An, Q. & Wang, H. Properties of traveling waves in an impulsive reaction–diffusion model with overcompensation. Z. Angew. Math. Phys. 74, 114 (2023). https://doi.org/10.1007/s00033-023-02004-x

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  • DOI: https://doi.org/10.1007/s00033-023-02004-x

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