title: Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons.
abstract: We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) [Formula: see text], which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on [Formula: see text], was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR [Formula: see text] of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR [Formula: see text] into the instantaneous population bursting rate [Formula: see text] (describing the bursting behavior) and the instantaneous population spike rate [Formula: see text] (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking "coherence factors" [Formula: see text] and [Formula: see text] of the bursting and spiking peaks in the power spectral densities of [Formula: see text] and [Formula: see text] (i.e., "signal to noise" ratio of the spectral peak height and its relative width). Through calculation of [Formula: see text] and [Formula: see text], we obtain the bursting and spiking thresholds beyond which the burst and spike synchronizations break up, respectively. Consequently, it is shown in explicit examples that the frequency-domain bursting and spiking order parameters may be usefully used for characterization of the bursting and the spiking transitions, respectively.
authors.affiliation: Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea.
authors.forename: Sang-Yoon
authors.initials: SY
authors.lastname: Kim
authors.affiliation: Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea.
authors.forename: Woochang
authors.initials: W
authors.lastname: Lim
keywords: Burst and spike synchronization transitions; Bursting neurons; Frequency-domain order parameters