Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations.

The minimal integrate-and-fire-or-burst neuron model succinctly describes both tonic firing and postinhibitory rebound bursting of thalamocortical cells in the sensory relay. Networks of integrate-and-fire-or-burst (IFB) neurons with slow inhibitory synaptic interactions have been shown to support stable rhythmic states, including globally synchronous and cluster oscillations, in which network-mediated inhibition cyclically generates bursting in coherent subgroups of neurons. In this paper, we introduce a reduced IFB neuronal population model to study synchronization of inhibition-mediated oscillatory bursting states to periodic excitatory input. Using numeric methods, we demonstrate the existence and stability of 1:1 phase-locked bursting oscillations in the sinusoidally forced IFB neuronal population model. Phase locking is shown to arise when periodic excitation is sufficient to pace the onset of bursting in an IFB cluster without counteracting the inhibitory interactions necessary for burst generation. Phase-locked bursting states are thus found to destabilize when periodic excitation increases in strength or frequency. Further study of the IFB neuronal population model with pulse-like periodic excitatory input illustrates that this synchronization mechanism generalizes to a broad range of n:m phase-locked bursting states across both globally synchronous and clustered oscillatory regimes.