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Propagation Dynamics in a Time Periodic Nonlocal Dispersal Model with Stage Structure

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Abstract

This paper is devoted to the study of propagation dynamics for a time periodic nonlocal dispersal model with stage structure. In the case where the birth rate function is monotone, we establish the existence of the spreading speed and its coincidence with the minimal wave speed for monotone periodic traveling waves by appealing to the theory developed for monotone semiflows. In the case where the birth rate function is non-monotone, we first obtain the spreading properties by the squeezing technique combined with some known results for the monotone case, and then investigate the existence of periodic traveling waves by using the asymptotic fixed point theorem due to the lack of parabolic estimates and compactness. Finally, we apply the general results to the Nicholson’s blowflies model for its spatial dynamics.

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Acknowledgements

We are grateful to the anonymous referee for his/her careful reading and valuable suggestions which led to an improvement of our original manuscript. W.-T. Li was partially supported by NSF of China (11671180, 11731005) and FRFCU (lzujbky-2016-ct12). J.-B. Wang was partially supported by FRFCU (162301182740, lzujbky-2016-226) and the China Scholarship Council (201606180060) under a joint-training program at Memorial University of Newfoundland when he was a Ph.D. student at Lanzhou University. X.-Q. Zhao was partially supported by the NSERC of Canada.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Wan-Tong Li

  2. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, People’s Republic of China

    Jia-Bing Wang

  3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

    Xiao-Qiang Zhao

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  1. Wan-Tong Li
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  2. Jia-Bing Wang
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  3. Xiao-Qiang Zhao
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Correspondence to Jia-Bing Wang.

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Li, WT., Wang, JB. & Zhao, XQ. Propagation Dynamics in a Time Periodic Nonlocal Dispersal Model with Stage Structure. J Dyn Diff Equat 32, 1027–1064 (2020). https://doi.org/10.1007/s10884-019-09760-3

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  • DOI: https://doi.org/10.1007/s10884-019-09760-3

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