Noise-induced multistability in the square root map

The effects of small-amplitude additive Gaussian white noise on the one-dimensional square root map are investigated. In particular, the focus is on the unexpected effects noise of varying amplitudes has on the system for parameter regions just outside intervals of multistability. It is shown that in these regions periodic behaviour that is unstable in the deterministic system can be effectively stabilised by the addition of noise of an appropriate amplitude. Features of noise-induced transitions from stable to stabilised unstable periodic behaviour are highlighted, and it is shown how these features can be understood by examining relative levels of expansion and contraction in the deterministic map.