  Cortical neurons are characterized by irregular firing and a broad
distribution of rates. The balanced state model explains these observations
with a cancellation of mean excitatory and inhibitory currents, which makes
fluctuations drive firing. In networks of neurons with current-based synapses,
the balanced state emerges dynamically if coupling is strong, i.e. if the mean
number of synapses per neuron $K$ is large and synaptic efficacy is of order
$1/\sqrt{K}$. When synapses are conductance-based, current fluctuations are
suppressed when coupling is strong, questioning the applicability of the
balanced state idea to biological neural networks. We analyze networks of
strongly coupled conductance-based neurons and show that asynchronous irregular
activity and broad distributions of rates emerge if synapses are of order
$1/\log(K)$. In such networks, unlike in the standard balanced state model,
current fluctuations are small and firing is maintained by a drift-diffusion
balance. This balance emerges dynamically, without fine tuning, if inputs are
smaller than a critical value, which depends on synaptic time constants and
coupling strength, and is significantly more robust to connection
heterogeneities than the classical balanced state model. Our analysis makes
experimentally testable predictions of how the network response properties
should evolve as input increases.
