论文标题
fkpp动力学由父域介导的延迟
FKPP dynamics mediated by a parent field with a delay
论文作者
论文摘要
我们研究了Fisher-Kolmogorov-Petrovsky-Piskunov（FKPP）过程的修改，其中扩散物质需要父母密度的繁殖场。一个生物学的例子是散射孢子（繁殖）的密度和固定真菌（父）的密度。父母以一定的速度产生繁殖体，繁殖体以另一种速度变成父物质。我们通过延迟通过FKPP过程对这种演变进行建模，这反映了新父母在开始产生繁殖之前成熟所需的有限时间。虽然过去已经将具有其他类型延迟的FKPP过程视为一种纯粹的数学结构，但在我们的工作中，FKPP模型的延迟会在自然科学环境中产生。显示所得密度前端的速度随着延迟时间的增加而降低，并且对繁殖率转化为父物质的速度具有不足的依赖性。值得注意的是，该模型中的前部总是比经典FKPP模型的Fisher波慢。最大的速度是经典值的一半，并且在零延迟和两个速率匹配时实现。
We examine a modification of the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) process in which the diffusing substance requires a parent density field for reproduction. A biological example would be the density of diffusing spores (propagules) and the density of a stationary fungus (parent). The parent produces propagules at a certain rate, and the propagules turn into the parent substance at another rate. We model this evolution by the FKPP process with delay, which reflects a finite time typically required for a new parent to mature before it begins to produce propagules. While the FKPP process with other types of delays have been considered in the past as a pure mathematical construct, in our work a delay in the FKPP model arises in a natural science setting. The speed of the resulting density fronts is shown to decrease with increasing delay time, and has a non-trivial dependence on the rate of conversion of propagules into the parent substance. Remarkably, the fronts in this model are always slower than Fisher waves of the classical FKPP model. The largest speed is half of the classical value, and it is achieved at zero delay and when the two rates are matched.
