Brain oscillations in a random neural network

It is well-known that rhythmic patterns of neural activity appear both in the normal and abnormal function of the brain. Apart from the standard bands of electric oscillations found in the electroencephalogram (EEG): from alpha (8–12 Hz) to delta waves (1–4 Hz), synchronized firing of neural populations characterize some complex cognitive functions such as memory, attention and consciousness. In the case of electrocardiogram (ECG) it is usually recognized that oscillations can be understood as the limit cycle of an underlying non-linear process in heart dynamics. However, the situation is not so clear for EEG and the origin and purpose of neural oscillations are still the subject of a heated debate.Our model is a version of the standard SIRS model from epidemiology in which susceptible, infected and recovered sites represent quiescent, firing and refractory neurons, respectively. Here we show that, in a SIRS random network epidemic model for neural activity, self-sustained oscillations appear in a restricted parameter region of the transition probabilities. This could explain the role of synchronized oscillations as a discriminant process for internal or external stimuli in brain dynamics.