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On the conjecture for the pushed wavefront to the diffusive Lotka–Volterra competition model

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Abstract

This paper concerns ecological invasion phenomenon of species based on the diffusive Lotka–Volterra competition model. We investigate the spreading speed (or the minimal wave speed of traveling waves) selection to the model and concentrate on the conjecture raised by Roques et al. (J Math Biol 71(2):465–489, 2015). By using an abstract implicit function theorem in a weighted functional space coupled with a perturbation technique, we not only prove this conjecture, but also show that the fast decay behavior of the first species is necessary and sufficient for the nonlinear speed selection of the whole system. This may lead to further significant results on the answer to the original Hosono’s conjecture, a problem that has been outstanding for more than twenty years.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Al-Hussein Bin Talal University, Ma’an, Jordan

    Ahmad Alhasanat

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

    Chunhua Ou

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  1. Ahmad Alhasanat
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  2. Chunhua Ou
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Correspondence to Ahmad Alhasanat.

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Chunhua Ou: This work is supported by the NSERC discovery Grant of Canada # 204509.

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Alhasanat, A., Ou, C. On the conjecture for the pushed wavefront to the diffusive Lotka–Volterra competition model. J. Math. Biol. 80, 1413–1422 (2020). https://doi.org/10.1007/s00285-020-01467-0

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  • DOI: https://doi.org/10.1007/s00285-020-01467-0

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