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Thermodynamic order parameters and statistical–mechanical measures for characterization of the burst and spike synchronizations of bursting neurons

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  • Kim, Sang-Yoon
  • Lim, Woochang

Abstract

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.

Suggested Citation

  • Kim, Sang-Yoon & Lim, Woochang, 2015. "Thermodynamic order parameters and statistical–mechanical measures for characterization of the burst and spike synchronizations of bursting neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 544-559.
  • Handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:544-559
    DOI: 10.1016/j.physa.2015.06.017
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    1. Anonymous, 2013. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 8(3), pages 243-243, December.
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    3. Shi, Xia & Lu, Qishao, 2009. "Burst synchronization of electrically and chemically coupled map-based neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2410-2419.
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    Cited by:

    1. Juan Carlos Jauregui-Correa & Carlos S. López-Cajun & Mihir Sen, 2017. "Determining the Coupling Source on a Set of Oscillators from Experimental Data," Complexity, Hindawi, vol. 2017, pages 1-10, May.
    2. Shaw, Pankaj Kumar & Chaubey, Neeraj & Mukherjee, S. & Janaki, M.S. & Iyengar, A.N. Sekar, 2019. "A continuous transition from chaotic bursting to chaotic spiking in a glow discharge plasma and its associated long range correlation to anti correlation behaviour," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 126-134.

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