Properties of traveling waves for integrodifference equations with nonmonotone growth functions

In this paper, we will establish some new properties of traveling waves for integrodifference equations with the nonmonotone growth functions. More precisely, for c ≥  c * , we show that either or that is, the wave converges to the positive equilibrium or oscillates about it at +∞. Sufficient condit...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2012-04, Vol.63 (2), p.249-259
Main Authors: Yu, Zhi-Xian, Yuan, Rong
Format: Article
Language:English
Subjects:
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
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Summary:In this paper, we will establish some new properties of traveling waves for integrodifference equations with the nonmonotone growth functions. More precisely, for c ≥  c * , we show that either or that is, the wave converges to the positive equilibrium or oscillates about it at +∞. Sufficient conditions can assure that both results will arise. We can also obtain that any traveling wave with wave speed c  >  c * possesses exponential decay at −∞. These results can be well applied to three types of growth functions arising from population biology. By choosing suitable parameter numbers, we can obtain the existence of oscillating waves. Our analytic results are consistent with some numerical simulations in Kot (J Math Biol 30:413–436, 1992 ), Li et al. (J Math Biol 58:323–338, 2009 ) and complement some known ones.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-011-0170-z