Neural field theory of plasticity in the cerebral cortex

A generalized timing-dependent plasticity rule is incorporated into a recent neural field theory to explore synaptic plasticity in the cerebral cortex, with both excitatory and inhibitory populations included. Analysis in the time and frequency domains reveals that cortical network behavior gives rise to a saddle-node bifurcation and resonant frequencies, including a gamma-band resonance. These system resonances constrain cortical synaptic dynamics and divide it into four classes, which depend on the type of synaptic plasticity window. Depending on the dynamical class, synaptic strengths can either have a stable fixed point, or can diverge in the absence of a separate saturation mechanism. Parameter exploration shows that time-asymmetric plasticity windows, which are signatures of spike-timing dependent plasticity, enable the richest variety of synaptic dynamics to occur. In particular, we predict a zone in parameter space which may allow brains to attain the marginal stability phenomena observed experimentally, although additional regulatory mechanisms may be required to maintain these parameters.