  We study inhibitory coherence (i.e., collective coherence by synaptic
inhibition) in an ensemble of globally-coupled type-I neurons which can fire at
arbitrarily low frequencies. No inhibitory coherence is observed in a
homogeneous ensemble composed of only subthreshold neurons (which cannot fire
spontaneously without noise). By increasing the fraction of (spontaneously
firing) suprathreshold neurons $P_{supra}$, heterogeneity-induced inhibitory
coherence is investigated in a heterogeneous ensemble of subthreshold and
suprathreshold neurons. As $P_{supra}$ passes a threshold $P_{supra}^*$,
suprathreshold neurons begin to synchronize and play the role of coherent
inhibitors for the emergence of inhibitory coherence. Thus,
regularly-oscillating ensemble-averaged global potential appears for $P_{supra}
> P_{supra}^*$. For this coherent case suprathreshold neurons exhibit coherent
mixed-mode oscillations with a fast subthreshold (small-amplitude) hopping
frequency and a lower spiking frequency. By virtue of their coherent
inhibition, sparsely synchronized suprathreshold neurons suppress noisy
activities of subthreshold neurons. Thus, only coherent subthreshold hoppings
appear in the individual potentials of subthreshold neurons. We also
characterize the inhibitory coherence in terms of the "statistical-mechanical"
spike-based and correlation-based measures and find that the degree of
inhibitory coherence increases with increasing $P_{supra}$ for $P_{supra} >
P_{supra}^*$. Finally, effect of sparse randomness of synaptic connectivity on
the inhibitory coherence and universality of the heterogeneity-induced
inhibitory coherence are briefly discussed.
