Bifurcation and oscillation in a time-delay neural mass model

The neural mass model developed by Lopes da Silva et al. simulates complex dynamics between cortical areas and is able to describe a limit cycle behavior for alpha rhythms in electroencephalography (EEG). In this work, we propose a modified neural mass model that incorporates a time delay. This time-delay model can be used to simulate several different types of EEG activity including alpha wave, interictal EEG, and ictal EEG. We present a detailed description of the model's behavior with bifurcation diagrams. Through simulation and an analysis of the influence of the time delay on the model's oscillatory behavior, we demonstrate that a time delay in neuronal signal transmission could cause seizure-like activity in the brain. Further study of the bifurcations in this new neural mass model could provide a theoretical reference for the understanding of the neurodynamics in epileptic seizures.