Noise-induced kinetic transition in two-component environment

Abstract

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.