On the approximation of finite-time Lyapunov exponents for the stochastic Burgers equation

Abstract

We analyze stochastic partial differential equations (SPDEs) with quadratic nonlinearities close to a change of stability. To this aim we compute finite-time Lyapunov exponents (FTLEs), observing a change of sign based on the interplay between the distance towards the bifurcation and the noise intensity. A technical challenge is to provide a suitable control of the nonlinear terms coupling the dominant and stable modes of the SPDE and of the corresponding linearization. In order to illustrate our results we apply them to the stochastic Burgers equation.