The problem of diffusion through the fluctuating medium, where processes of substance disintegration and reproduction are possible, was posed at the end of the last century. It was established that the action of multiplicative external noise on a system can result in qualitative reorganization of its dynamical behavior. When such reorganization leads to the appearance of a new stationary dynamic mode, it is customary to speak about a noise-induced phase or kinetic transition. In this paper the noise-induced kinetic transition in two-component environment where the interacting components have contrasting lifetimes and diffusion coefficients is considered. It is shown that the presence of an additional long-lived component can lead to a dramatic decrease in the system generation threshold. We called this effect the depository reproduction. Analytical consideration of the diffusion process in a fluctuating medium causes enormous difficulties even for a single component substance. Meanwhile, in some cases of practical interest, the problem consideration can be conducted using stochastic geometry and percolation theory in particular. In the present work the noise-induced kinetic transition in two-component distributed systems is studied by the tools of directed percolation. To present the depository reproduction effect more vividly we use a new numeral grossone that allows to express different infinitesimal and infinite numerals. It was shown that the reverse conversion of the long-lived component to the short-lived one ensures the survival of the system at significantly lower concentrations of production centers.

在上世纪末提出了通过波动介质扩散的问题，其中物质可能会分解和繁殖。可以确定，外部噪声在系统上的作用可以导致其动态行为的定性重组。当这种重组导致出现新的平稳动态模式时，通常会谈论噪声引起的相位或动力学转变。在本文中，考虑了在两组分环境中由噪声引起的动力学转变，其中相互作用的组分具有相反的寿命和扩散系数。结果表明，存在额外的长寿命组件会导致系统生成阈值急剧下降。我们称这种效应为存托繁殖。对波动介质中扩散过程的分析考虑，即使对于单一成分的物质也造成巨大的困难。同时，在某些实际感兴趣的情况下，可以使用随机几何和渗流理论特别地进行问题考虑。在当前的工作中，通过定向渗滤工具研究了两组分分布系统中的噪声诱导的动力学转变。为了更生动地呈现存放地的复制效果，我们使用了新的数字grosson允许表达不同的无穷小数字和无穷大数字。结果表明，长寿命组分向短寿命组分的逆向转化确保了系统在低得多的生产中心集中度下的生存。