Slow manifold reduction of a stochastic chemical reaction: Exploring keizer's paradox

Abstract

Keizer's paradox refers to the observation that deterministic and stochastic descriptions of chemical reactions can predict vastly different long term outcomes. In this paper, we use slow manifold analysis to help resolve this paradox for four variants of a simple autocatalytic reaction. We also provide rigorous estimates of the spectral gap of important linear operators, which establishes parameter ranges in which the slow manifold analysis is appropriate.