Giant amplification of noise in fluctuation-induced pattern formation

TL;DR

This paper demonstrates that intrinsic noise can cause giant amplification of patterns in spatially-extended systems, making fluctuation-induced patterns observable without fine-tuning, due to the interplay of noise and system eigenvectors.

Contribution

It reveals a mechanism where intrinsic noise leads to large amplitude patterns through transient growth, broadening understanding of biological pattern formation.

Findings

Intrinsic noise can produce giant amplification of patterns.

Amplified patterns are comparable to deterministic Turing patterns.

The mechanism does not require fine-tuning of parameters.

Abstract

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially-extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and non-orthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism provides a robust basis for fluctuation-induced biological pattern formation based on the Turing mechanism, without requiring fine tuning of diffusion constants.