  We analyze a pair of delay-coupled FitzHugh-Nagumo oscillators exhibiting
in-out intermittency as a part of the generating mechanism of extreme events.
We study in detail the characteristics of in-out intermittency and identify the
invariant subsets involved --- a saddle fixed point and a saddle periodic orbit
--- neither of which are chaotic as in the previously reported cases of in-out
intermittency. Based on the analysis of a periodic attractor possessing in-out
dynamics, we can characterize the approach to the invariant synchronization
manifold and the spiralling out to the saddle periodic orbit with subsequent
ejection from the manifold. Due to the striking similarities, this analysis of
in-out dynamics explains also in-out intermittency.
