Abstract
In the present paper, we study the stochastically-induced behavior of a
non-linear volcanic model containing three prognostic variables: the
plug velocity $u$, the pressure under the plug, and the conduit volume
$V$. The nouvelle phenomena of noise-induced transitions from the
equilibrium to the cycle in the bistability parametric zone and
noise-induced excitement with the generation of spike oscillations in
the monostability zone are found in the presence of N-shaped friction
force. To study these phenomena numerically, we used the computations of
random solutions, the phase trajectories and time series, the statistics
of interspike intervals, and the mean square variations. To study these
phenomena analytically, we applied the stochastic sensitivity function
technique and the confidence domains method. This approach is used to
predict the noise-induced transition from a “dormant volcano” state to
the “active volcano” mode. From the physical point of view, the
volcano is capable to become active under the influence of external
noises in the friction force, which model various compositions and
properties of volcanic rocks. What is more, the volcanic plug can pop
out when it is slipping heavily, and the volcano can erupt.