  We report the emergence of explosive synchronization in a multiplex network
where oscillators on the first layer are coupled with attractive coupling and
those on the second layer, coupled with repulsive coupling. With Stuart-Landau
and FitzHugh-Nagumo oscillators as the nodal dynamics, we consider non-local
and mean-field intralayer couplings. We establish that explosive
synchronization occurs in the multiplex network in the presence of Gaussian
noise, and the transition is first order with hysteresis to a state of complete
intra-layer and in-phase interlayer synchronization. The width of the
hysteresis depends on the range of intralayer attractive coupling, strength of
interlayer coupling and noise. We also see how to have control over this
induced transition so that the explosive nature, if undesirable, can be
converted to continuous type by tuning the strength of repulsive coupling or
noise.
