Existence of traveling waves for integral recursions with nonmonotone growth functions
Existence of traveling waves for integral recursions with nonmonotone growth functions
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DOI：
10.1007/s00285-008-0175-1
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发表时间：
2009-03-01
影响因子：
1.9
通讯作者：
Weinberger, Hans F.
中科院分区：
文献类型：
--
作者：
Li, Bingtuan;Lewis, Mark A.;Weinberger, Hans F.
研究了一类单种群同步增长与扩散的积分递推模型。众所周知，如果在繁殖函数中没有过补偿，则递归具有渐近扩展速度c*，并且该速度可以表征为最慢的非常数行波解的速度。利用Thieme（J Reine Angew Math 306：94-121，1979）为研究流行病的时空积分方程模型而引入的思想，可以找到一类仍具有渐近传播速度的具有过补偿的积分递归。目前的工作给出了一个大的子类，这些模型与过补偿的传播速度仍然可以被描述为一个非恒定的行波的最慢速度。为了说明我们的结果，我们数值模拟了一系列的行波。模拟结果表明，根据繁殖力函数的性质，波浪的尾部可以单调地接近承载能力，可以以振荡的方式接近承载能力，或者可以围绕承载能力不断振荡，其值由可计算的正数上下限定。
A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with overcompensation which still have asymptotic spreading speeds can be found by using the ideas introduced by Thieme (J Reine Angew Math 306:94-121, 1979) for the study of space-time integral equation models for epidemics. The present work gives a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. To illustrate our results, we numerically simulate a series of traveling waves. The simulations indicate that, depending on the properties of the fecundity function, the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers.