  Experimental and numerical results suggest that the brain can be viewed as a
system acting close to a critical point, as confirmed by scale-free
distributions of relevant quantities in a variety of different systems and
models. Less attention has received the investigation of the temporal
correlation functions in brain activity in different, healthy and pathological,
conditions. Here we perform this analysis by means of a model with short and
long-term plasticity which implements the novel feature of different recovery
rates for excitatory and inhibitory neurons, found experimentally. We evidence
the important role played by inhibitory neurons in the supercritical state: We
detect an unexpected oscillatory behaviour of the correlation decay, whose
frequency depends on the fraction of inhibitory neurons and their connectivity
degree. This behaviour can be rationalized by the observation that bursts in
activity become more frequent and with a smaller amplitude as inhibition
becomes more relevant.
