Lyapunov exponents and synchronisation by noise for systems of SPDEs

TL;DR

This paper provides quantitative estimates for Lyapunov exponents in stochastic reaction-diffusion systems, demonstrating noise-induced synchronization through rigorous analysis of invariant measures.

Contribution

It introduces new methods to estimate Lyapunov exponents for SPDEs with degenerate potentials and establishes synchronization by noise for the first time in this context.

Findings

Quantitative bounds on top Lyapunov exponents for SPDEs.

Proof of synchronization by noise in reaction-diffusion systems.

Asymptotic expansion technique for invariant measures.

Abstract

Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time.