  It has been recently reported that explosive synchronization transitions can
take place in networks of phase oscillators [G\'omez-Garde\~nes \emph{et al.}
Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et
al.} Phys.Rev.Letts. 108, 168702 (2012)]. Here, we investigate the effect of a
microscopic correlation between the dynamics and the interacting topology of
coupled FitzHugh-Nagumo oscillators on phase synchronization transition in
Barab\'asi-Albert (BA) scale-free networks and Erd\"os-R\'enyi (ER) random
networks. We show that, if the width of distribution of natural frequencies of
the oscillations is larger than a threshold value, a strong hysteresis loop
arises in the synchronization diagram of BA networks due to the positive
correlation between node degrees and natural frequencies of the oscillations,
indicating the evidence of an explosive transition towards synchronization of
relaxation oscillators system. In contrast to the results in BA networks, in
more homogeneous ER networks the synchronization transition is always of
continuous type regardless of the the width of the frequency distribution.
Moreover, we consider the effect of degree-mixing patterns on the nature of the
synchronization transition, and find that the degree assortativity is
unfavorable for the occurrence of such an explosive transition.
