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Spreading speeds and traveling waves in competitive recursion systems

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Abstract

This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual population densities at the coexistence domain are lower than the case when the competition vanishes.

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Authors and Affiliations

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

    Guo Lin & Wan-Tong Li

  2. Department of Mathematics, University of Miami, P. O. Box 249085, Coral Gables, FL, 33124-4250, USA

    Shigui Ruan

Authors
  1. Guo Lin
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  2. Wan-Tong Li
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  3. Shigui Ruan
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Correspondence to Guo Lin.

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Lin, G., Li, WT. & Ruan, S. Spreading speeds and traveling waves in competitive recursion systems. J. Math. Biol. 62, 165–201 (2011). https://doi.org/10.1007/s00285-010-0334-z

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  • DOI: https://doi.org/10.1007/s00285-010-0334-z

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