Hebbian plasticity and homeostasis in a model of hypercolumn of the visual cortex.

Neurons in the nervous system display a wide variety of plasticity processes. Among them are covariance-based rules and homeostatic plasticity. By themselves, the first ones tend to generate instabilities because of the unbounded potentiation of synapses. The second ones tend to stabilize the system by setting a target for the postsynaptic firing rate. In this work, we analyze the combined effect of these two mechanisms in a simple model of hypercolumn of the visual cortex. We find that the presence of homeostatic plasticity together with nonplastic uniform inhibition stabilizes the effect of Hebbian plasticity. The system can reach nontrivial solutions, where the recurrent intracortical connections are strongly modulated. The modulation is strong enough to generate contrast invariance. Moreover, this state can be reached even beginning from a weakly modulated initial condition.