Analysis of noise-induced eruptions in a geyser model

Abstract

Motivated by important geophysical applications we study a non-linear model of geyser dynamics under the influence of external stochastic forcing. It is shown that the deterministic dynamics is substantially dependent on system parameters leading to the following evolutionary scenaria: (i) oscillations near a stable equilibrium and a transient tendency of the phase trajectories to a spiral sink or a stable node (pre-eruption regime), and (ii) fast escape from equilibrium (eruption regime). Even a small noise changes the system dynamics drastically. Namely, a low-intensity noise generates the small amplitude stochastic oscillations in the regions adjoining to the stable equilibrium point. A small buildup of noise intensity throws the system over its separatrix and leads to eruption. The role of the friction coefficient and relative pressure in the deterministic and stochastic dynamics is studied by direct numerical simulations and stochastic sensitivity functions technique.