Abstract
Intrinsic or demographic noise has been shown to play an important role in
the dynamics of a variety of systems including predator-prey populations,
intracellular biochemical reactions, and oscillatory chemical reaction systems,
and is known to give rise to oscillations and pattern formation well outside
the parameter range predicted by standard mean-field analysis. Initially
motivated by an experimental model of cells and tissues where the cells are
represented by chemical reagents isolated in emulsion droplets, we study the
stochastic Brusselator, a simple activator-inhibitor chemical reaction model.
Our work builds on the results of recent studies and looks to understand the
role played by intrinsic fluctuations when the timescale of the inhibitor
species is fast compared to that of the activator. In this limit, we observe a
noise induced switching between small and large amplitude oscillations that
persists for large system sizes (N), and deep into the non oscillatory part of
the mean-field phase diagram. We obtain a scaling relation for the first
passage times between the two oscillating states. From our scaling function, we
show that the first passage times have a well defined form in the large N
limit. Thus in the limit of small noise and large timescale separation a
careful treatment of the noise will lead to a set of non-trivial deterministic
equations different from those obtained from the standard mean-field limit.