  The brain is characterized by a strong heterogeneity of inhibitory neurons.
We report that spiking neural networks display a resonance to the heterogeneity
of inhibitory neurons, with optimal input/output responsiveness occurring for
levels of heterogeneity similar to that found experimentally in cerebral
cortex. A heterogeneous mean-field model predicts such optimal responsiveness.
Moreover, we show that new dynamical regimes emerge from heterogeneity that
were not present in the equivalent homogeneous system, such as sparsely
synchronous collective oscillations.
