  In [1], we have shown that the dynamics of an interconnected population of
excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens
(BT)bifurcation point can generate the observed scale-free avalanches at the
population level and the highly variable spike patterns of individual neurons.
These characteristics match experimental findings for spontaneous intrinsic
activity in the brain. In this paper, we address the mechanisms causing the
system to get and remain near this BT point. We propose an effective stochastic
neural field model which captures the dynamics of the mean-field model. We show
how the network tunes itself through local long-term synaptic plasticity by
STDP and short-term synaptic depression to be close to this bifurcation point.
The mesoscopic model that we derive matches the directed percolation model at
the absorbing state phase transition.
