Mode locking in a periodically forced integrate-and-fire-or-burst neuron model - art. no. 041914

The minimal "integrate-and-fire-or-burst" (IFB) neuron model reproduces the salient features of experimentally observed thalamocortical relay neuron r esponse properties, including the temporal tuning of both tonic spiking (i. e., conventional action potentials) and post-inhibitory rebound bursting me diated by the low-threshold Ca2+ current, I-T. In previous work focusing on experimental and IFB model responses to sinusoidal current injection, larg e regions of stimulus parameter space were observed for which the response was entrained to periodic applied current, resulting in repetitive burst, t onic, or mixed (i.e., burst followed by tonic) responses. Here we present a n exact analysis of such mode-locking in the integrate-and-fire-or-burst mo del under the influence of arbitrary periodic forcing that includes sinusoi dally driven responses as one case. In this analysis, the instabilities of mode-locked states are identified as both smooth bifurcations of an associa ted firing time map and nonsmooth bifurcations of the underlying discontinu ous flow. The explicit construction of borders in parameter space that defi ne the instabilities of mode-locked zones is used to build up the Arnol'd t ongue structure for the model. The zones for mode-locking are shown to be i n excellent agreement with numerical simulations and are used to explore th e observed stimulus dependence of burst versus tonic response of the IFB ne uron model.