  We study the effects of periodic subthreshold pacemaker activity and
time-delayed coupling on stochastic resonance over scale-free neuronal
networks. As the two extreme options, we introduce the pacemaker respectively
to the neuron with the highest degree and to one of the neurons with the lowest
degree within the network, but we also consider the case when all neurons are
exposed to the periodic forcing. In the absence of delay, we show that an
intermediate intensity of noise is able to optimally assist the pacemaker in
imposing its rhythm on the whole ensemble, irrespective to its placing, thus
providing evidences for stochastic resonance on the scale-free neuronal
networks. Interestingly thereby, if the forcing in form of a periodic pulse
train is introduced to all neurons forming the network, the stochastic
resonance decreases as compared to the case when only a single neuron is paced.
Moreover, we show that finite delays in coupling can significantly affect the
stochastic resonance on scale-free neuronal networks. In particular,
appropriately tuned delays can induce multiple stochastic resonances
independently of the placing of the pacemaker, but they can also altogether
destroy stochastic resonance. Delay-induced multiple stochastic resonances
manifest as well-expressed maxima of the correlation measure, appearing at
every multiple of the pacemaker period. We argue that fine-tuned delays and
locally active pacemakers are vital for assuring optimal conditions for
stochastic resonance on complex neuronal networks.
