Wave propagation for a two-component lattice dynamical system arising in strong competition models |
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Authors: | Jong-Shenq Guo Chang-Hong Wu |
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Institution: | a Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137, Taiwan b Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan |
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Abstract: | We study a Lotka-Volterra type competition system with bistable nonlinearity in which the habitat is divided into discrete niches. We show that there exist non-monotone stationary solutions when the migration coefficients are sufficiently small. Also, we prove that the propagation failure phenomenon occurs. Finally, we focus on the traveling wave with nonzero wave speed. By investigating the asymptotic behavior of tails of wave profiles, we show that nonzero speed wave profiles are monotone. Moreover, the nonzero wave speed is unique in the sense that the wave cannot propagate with two different nonzero wave speeds. |
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Keywords: | primary 34K05 34A34 secondary 34K60 34E05 |
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