  We are interested in characterization of population synchronization of
bursting neurons which exhibit both the slow bursting and the fast spiking
timescales, in contrast to spiking neurons. Population synchronization may be
well visualized in the raster plot of neural spikes which can be obtained in
experiments. The instantaneous population firing rate (IPFR) $R(t)$, which may
be directly obtained from the raster plot of spikes, is often used as a
realistic collective quantity describing population behaviors in both the
computational and the experimental neuroscience. For the case of spiking
neurons, realistic thermodynamic order parameter and statistical-mechanical
spiking measure, based on $R(t)$, were introduced in our recent work to make
practical characterization of spike synchronization. Here, we separate the slow
bursting and the fast spiking timescales via frequency filtering, and extend
the thermodynamic order parameter and the statistical-mechanical measure to the
case of bursting neurons. Consequently, it is shown in explicit examples that
both the order parameters and the statistical-mechanical measures may be
effectively used to characterize the burst and spike synchronizations of
bursting neurons.
