  We consider a stochastic version of the so-called Brusselator - a
mathematical model for a two-dimensional chemical reaction network - in which
one of its parameters is assumed to vary randomly. It has been suggested via
numerical explorations that the system exhibits noise-induced synchronization
when time goes to infinity. Complementing this perspective, in this work we
explore some of its finite-time features from a random dynamical systems
perspective. In particular, we focus on the deviations that orbits of
neighboring initial conditions exhibit under the influence of the same noise
realization. For this, we explore its local instabilities via finite-time
Lyapunov exponents. Furthermore, we present the stochastic Brusselator as a
fast-slow system in the case that one of the parameters is much larger than the
other one. In this framework, an apparent mechanism for generating the
stochastic instabilities is revealed, being associated to the transition
between the slow and fast regimes.
