  In the cerebral cortex, neurons are subject to a continuous bombardment of
synaptic inputs originating from the network's background activity. This leads
to ongoing, mostly subthreshold membrane dynamics that depends on the
statistics of the background activity and of the synapses made on a neuron.
Subthreshold membrane polarization is, in turn, a potent modulator of neural
responses. The present paper analyzes the subthreshold dynamics of the neural
membrane potential driven by synaptic inputs of stationary statistics. Synaptic
inputs are considered in linear interaction. The analysis identifies regimes of
input statistics which give rise to stationary, fluctuating, oscillatory, and
unstable dynamics. In particular, I show that (i) mere noise inputs can drive
the membrane potential into sustained, quasiperiodic oscillations (noise-driven
oscillations), in the absence of a stimulus-derived, intraneural, or network
pacemaker; (ii) adding hyperpolarizing to depolarizing synaptic input can
increase neural activity (hyperpolarization-induced activity), in the absence
of hyperpolarization-activated currents.
