Effects of intrinsic fluctuations in a prototypical chemical oscillator: metastability and switching (1303.3048v1)

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.