  The activity in the brain cortex remarkably shows a simultaneous presence of
robust collective oscillations and neuronal avalanches, where intermittent
bursts of pseudo-synchronous spiking are interspersed with long periods of
quiescence. The mechanisms allowing for such a coexistence are still a matter
of an intensive debate. Here, we demonstrate that avalanche activity patterns
can emerge in a rather simple model of an array of diffusively coupled neural
oscillators with multiple timescale local dynamics in vicinity of a canard
transition. The avalanches coexist with the fully synchronous state where the
units perform relaxation oscillations. We show that the mechanism behind the
avalanches is based on an inhibitory effect of interactions, which may quench
the spiking of units due to an interplay with the maximal canard. The avalanche
activity bears certain heralds of criticality, including scale-invariant
distributions of event sizes. Furthermore, the system shows an increased
sensitivity to perturbations, manifested as critical slowing down and a reduced
resilience.
