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We are interested in characterization of population synchronization ofbursting neurons which exhibit both the slow bursting and the fast spikingtimescales, in contrast to spiking neurons. Population synchronization may bewell visualized in the raster plot of neural spikes which can be obtained inexperiments. The instantaneous population firing rate (IPFR) $R(t)$, which maybe directly obtained from the raster plot of spikes, is often used as arealistic collective quantity describing population behaviors in both thecomputational and the experimental neuroscience. For the case of spikingneurons, realistic thermodynamic order parameter and statistical-mechanicalspiking measure, based on $R(t)$, were introduced in our recent work to makepractical characterization of spike synchronization. Here, we separate the slowbursting and the fast spiking timescales via frequency filtering, and extendthe thermodynamic order parameter and the statistical-mechanical measure to thecase of bursting neurons. Consequently, it is shown in explicit examples thatboth the order parameters and the statistical-mechanical measures may beeffectively used to characterize the burst and spike synchronizations ofbursting neurons.

Thermodynamic Order Parameters and Statistical-Mechanical Measures for Characterization of the Burst and Spike Synchronizations of Bursting Neurons