Dynamical phase transitions in periodically driven model neurons

Transitions between dynamical states in integrate-and-fire neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a kind of phase transition intermediate between continuous and first order. In the model-independent spirit of our analysis we show that a six-dimensional (6D) gating variable model with an attracting limit cycle has similar phase transitions, governed by a 1D return map. This reduction to 1D map dynamics should extend to real neurons in a periodic current clamp setting.