Evaluation of entrainment of a nonlinear neural oscillator to white noise

The Lyapunov exponent for a one-dimensional neural oscillator model, the theta neuron, is computed for white noise forcing, using the steady-state solution to the associated Fokker-Planck equation. The latter is mildly singular, due to the nature of the multiplicative input. In agreement with previous results with similar models, the exponent is negative for all forcing amplitudes, but here it is shown to be small, relative to that for periodic drive, in a range of forcing strengths. Thus the synchronization of an ensemble of independent neurons receiving common but random input can be slow. Moreover, this implies that aperiodic input may be suboptimal, in some contexts, for preserving the reliability of fine spike timing, a potentially important component of the neural "code."