  The cellular automaton model of Piegari, Di Maio, Scandone and Milano, J.
Volc. Geoth. Res., 202, 22-28 (2011) is extended to include magma-induced
stress (i.e. a local magma-related augmentation of the stress field). This
constitutes a nonlinear coupling between the magma and stress fields considered
by this model, which affects the statistical distributions of eruptions
obtained. The extended model retains a power law relation between eruption size
and frequency for most events, as expected from the self organised criticality
inspiring this model; but the power law now applies for a reduced range of
size, and there are new peaks of relatively more frequent eruptions of
intermediate and large size. The cumulative frequency of repose time between
events remains well modelled by a stretched exponential function of repose time
(approaching a pure exponential distribution only for the longest repose
times), but the time scales of this behaviour are slightly longer, reflecting
the increased preference for larger events. The eruptions are relatively more
likely to have high volatile (water) content, so would generally be more
explosive. The new model also naturally favours a central `axial' transport
conduit, as found in many volcano systems, but which otherwise must be
artificially imposed within such models.
