Mean-Field Descriptions of Bursting Behavior in Networks of Spiking Neurons
Development and validation of mean-field models of spiking neural networks, studying phase transitions between asynchronous and synchronized bursting behavior.
This project is aimed at the development and validation of mean-field models of spiking neural networks. Such mean-field models represent direct mathematical descriptions of the macroscopic dynamics of a neural population and are beneficial for both the mathematical analysis of emergent behavior within a population and studies of larger networks of interconnected populations (see Fig. 1). Thus, mean-field models are an important tool for studying phase transitions in basal ganglia networks.
In a first step, we extended a mean-field model of globally coupled quadratic integrate-and-fire (QIF) neurons (see ) with different short-term adaptation mechanisms and examined their effects on the population dynamics via bifurcation analysis . For the latter, we used the Python interface to the bifurcation software Auto-07p that comes with our self-developed dynamical systems software PyRates . We found regimes of bursting behavior that emerged due to short-term adaptation in our model. Furthermore, we found a close correspondence between the mean-field model and spiking neural networks of different size and coupling density. In Fig. 2, we show the difference between the mean-field model and different spiking neural networks in terms of bursting frequency and amplitude.
 Montbrió E, Pazó D, Roxin A. Macroscopic Description for Networks of Spiking Neurons. Physical Review X. 2015; 5(2): 021028.
 Gast R, Helmut S, Knösche TR. A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation. bioRxiv. 2019; p. 806273. doi:10.1101/806273.
 Gast R, Rose D, Salomon C, Möller HE, Weiskopf N, Knösche TR. PyRates— A Python framework for rate-based neural simulations. PLOS ONE.2019; 14(12): e0225900. doi:10.1371/journal.pone.0225900.