The dynamics of autocatalytic agents in noisy environment is a basic mechanism in many branches of natural and social sciences. In particular the emergence of localized objects with complex adaptive properties is a common feature not explained by PDE based pattern formation theories. In former works we have established a new concept for the study of this field, namely, adaptation of autocatalytic fluctuations to noise. The emergence of dynamical phase transition through the combination of fluctuations and autoreactivity has been demonstrated theoretically and by numerical simulations. These results were further analyzed by mathematicians. Their theorems imply a distinction between the typical and the average behavior and emphasize the rule of rare events. While the initial model was very abstract, it appears to capture the essence of the accelerated growth in noisy environments, and it attracts interest from experts in various fields. Moreover, our current results show that noise induced adaptation exists in a wider range of models. We hereby propose a theoretical and experimental extension of our models to real phenomena. The suggested study involves an analysis of pattern formation and adaptation in noisy reactive systems. Effects of single/multi species competition, external sources and non-Brownian stochastic dynamics are to be considered and applied to the wide range of problems. Techniques, adapted from physics and mathematics, together with numerical simulations, will be used to analyze the behavior of experimental systems.
The systems that we will study are: