  The phase-resetting curve (PRC) describes the response of a neural oscillator
to small perturbations in membrane potential. Its usefulness for predicting the
dynamics of weakly coupled deterministic networks has been well characterized.
However, the inputs to real neurons may often be more accurately described as
barrages of synaptic noise. Effective connectivity between cells may thus arise
in the form of correlations between the noisy input streams. We use constrained
optimization and perturbation methods to prove that PRC shape determines
susceptibility to synchrony among otherwise uncoupled noise-driven neural
oscillators. PRCs can be placed into two general categories: Type I PRCs are
non-negative while Type II PRCs have a large negative region. Here we show that
oscillators with Type II PRCs receiving common noisy input sychronize more
readily than those with Type I PRCs.
