Gamma oscillations are thought to play a role in information processing in the brain. Bursting neurons, which exhibit periodic clusters of spiking activity, are a type of neuron that are thought to contribute largely to gamma oscillations. However, little is known about how the properties of bursting neurons affect the emergence of gamma oscillation, its waveforms, and its synchronized characteristics, especially when subjected to stochastic fluctuations. In this study, we proposed a bursting neuron model that can analyze the bursting ratio and the phase response function. Then we theoretically analyzed the neuronal population dynamics composed of bursting excitatory neurons, mixed with inhibitory neurons. The bifurcation analysis of the equivalent Fokker-Planck equation exhibits three types of gamma oscillations of unimodal firing, bimodal firing in the inhibitory population, and bimodal firing in the excitatory population under different interaction strengths. The analyses of the macroscopic phase response function by the adjoint method of the Fokker-Planck equation revealed that the inhibitory doublet facilitates synchronization of the high-frequency oscillations. When we keep the strength of interactions constant, decreasing the bursting ratio of the individual neurons increases the relative high-gamma component of the populational phase-coupling functions. This also improves the ability of the neuronal population model to synchronize with faster oscillatory input. The analytical frameworks in this study provide insight into nontrivial dynamics of the population of bursting neurons, which further suggest that bursting neurons have an important role in rhythmic activities.

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