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Asymptotic stability of monostable wavefronts in discrete-time integral recursions

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Abstract

The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ2. We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior. Then, by employing the comparison principle and upper and lower solutions technique, we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation. We also obtain some similar results in ℝ.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China

    Guo Lin & WanTong 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. WanTong Li
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  3. ShiGui Ruan
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Correspondence to ShiGui Ruan.

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Lin, G., Li, W. & Ruan, S. Asymptotic stability of monostable wavefronts in discrete-time integral recursions. Sci. China Math. 53, 1185–1194 (2010). https://doi.org/10.1007/s11425-009-0123-6

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  • DOI: https://doi.org/10.1007/s11425-009-0123-6

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