A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

Abstract

Bursting plays an important role in neural communication. At the population level, macro-scopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of such phase transitions, mean-field descriptions of macroscopic bursting behavior pose a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons in which collective bursting behavior arises via short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. We characterize the emerging bursting behavior using bifurcation analysis and validate our mean-field derivations by comparing the microscopic and macroscopic descriptions of the population dynamics. Hence, we provide mechanistic descriptions of phase transitions between bursting and non-bursting population dynamics which play important roles in both healthy neural communication and neurological disorders.