Abstract
How do environmental heterogeneity influence propagation dynamics of the age-structured invasive species? We investigate this problem by considering a yearly generation invasive species in time-space periodic habitat. Starting from an age-structured population growth law, we formulate a reaction-diffusion model with time-space periodic dispersal, mortality and recruitment. Thanks to the fundamental solution for linear part of the model, we reduce to study the dynamics of a time-space periodic semiflow which is defined by the solution map. By the recent developed dynamical theory in Fang et al. (J Funct Anal 272:4222-4262, 2017), we obtained the spreading speed and its coincidence with the minimal wave speed of time-space periodic traveling waves, as well as the variational characterization of spreading speed in terms of a principal eigenvalue problem. Such results are also proved back to the reaction-diffusion model.
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Acknowledgements
This work received fundings from the NSF of China (12001533, 11771108). We are very grateful to the anonymous referee for careful reading and valuable comments, which led to an improvement of the original manuscript.
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Pan, Y. Propagation dynamics for an age-structured population model in time-space periodic habitat. J. Math. Biol. 84, 19 (2022). https://doi.org/10.1007/s00285-022-01721-7
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DOI: https://doi.org/10.1007/s00285-022-01721-7