Extreme events in FitzHugh-Nagumo oscillators coupled with two time delays

We study two identical FitzHugh-Nagumo oscillators which are coupled with one or two different time delays. If only a single-delay coupling is used, the length of the delay determines whether the synchronization manifold is transversally stable or unstable, exhibiting mixed-mode or chaotic oscillations in which the small amplitude oscillations are always in phase but the large amplitude oscillations are in phase or out of phase, respectively. For two delays we find an intricate dynamics which comprises an irregular alteration of small amplitude oscillations, in-phase and out-of-phase large amplitude oscillations, also called extreme events. This transient chaotic dynamics is sandwiched between a bubbling transition and a blowout bifurcation.