Propagation and its failure in a lattice delayed differential equation with global interaction |
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Authors: | Shiwang Ma |
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Institution: | a Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, PR China b Department of Applied Mathematics, University of Western Ontario, London, Ont., Canada N6A 5B7 |
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Abstract: | We study the existence, uniqueness, global asymptotic stability and propagation failure of traveling wave fronts in a lattice delayed differential equation with global interaction for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. In the bistable case, under realistic assumptions on the birth function, we prove that the equation admits a strictly monotone increasing traveling wave front. Moreover, if the wave speed does not vanish, then the wave front is unique (up to a translation) and globally asymptotic stable with phase shift. Of particular interest is the phenomenon of “propagation failure” or “pinning” (that is, wave speed c = 0), we also give some criteria for pinning in this paper. |
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Keywords: | 34K30 35B40 35R10 58D25 |
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