Lyapunov exponents and synchronisation by noise for systems of SPDEs

2022/07/20 by B. Gess, Gess, B., P. Tsatsoulis +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · #35K57 #37H15 #37L30 #60H15 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2207.09820

openalex publication_date 2022/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Cited by

• Synchronization by degenerate noise

Related

• On the negativity of the top Lyapunov exponent for stochastic differential equations driven by fractional Brownian motion
• Quantitative instability for stochastic scalar reaction-diffusion equations
• Rigorous enclosure of Lyapunov exponents of stochastic flows
• Lyapunov exponents in a slow environment
• Lower bounds on the top Lyapunov exponent for linear PDEs driven by the 2D stochastic Navier-Stokes equations