Phase Locking and Resonances for Stochastic Excitable Systems

We investigate the phase locking of firing events in periodically forced stochastic excitable systems. Our study is motivated by the observation of randomly phase locked firing activity in a large number of neurons, especially those involved in transducing physical stimuli such as temperature, sound, pressure and electric fields. The purpose of our paper is to review our work on the biophysical origin of such firing patterns. Special attention is given to the constructive effect of noise, and to the connection between stochastic and deterministic resonances in such systems. We present new results on stochastic phase locking in the subthreshold and suprathreshold regimes, and on the non-monotonicity of the spectral amplification as a function of noise intensity. We also discuss current outstanding problems and potentially fruitful future research directions.