Phase diagram analysis of noise-induced transition in an autocatalytic reaction

We present the analysis of the genetic model of autocatalytic chemical reactions proposed by Arnold et al. This model, when subjected to multiplicative white noise modelling environmental fluctuations, can undergo a sudden change from a unimodal state to a bimodal one, while no such transition occurs if the noise is absent. Here, this noise-induced transition is studied analytically by investigating the so-called critical surface in the three-dimensional parameter space.