2.1 Introduction

One of the most important features of the BCM theory, is the sliding modification threshold, ? _M, the cross-over point at which synaptic modification changes sign. Cooper, Liberman and Oja (1979) (CLO) introduced the idea that synaptic modification changes sign at a cross-over point they called the modification threshold. According to CLO, for cell activity above threshold, modification follows a classical Hebbian rule; for cell activity below threshold, modification is anti-Hebbian. This means that only patterns that elicit high post-synaptic activity (beyond the threshold ? _M) will have their concurrently active synapses strengthened (the Hebbian region), while active synapses which elicit post-synaptic activity, but fail to elicit strong enough activity, will have their synapses weakened (non-Hebbian region). BCM added the idea that this modification threshold moves as some function of cell activity. If this function is properly non-linear, the theory is stabilized, because the threshold moves quickly enough to catch up to the cell activity caused by increasing or decreasing weights.

Extensive simulations are usually required to compare this theory with experiment in real world situations. In these simulations, the logical connections between assumptions and conclusions are sometimes obscured by the many parameters and the complexity of the data. Thus it is of great value to analyze systems that are simple enough so that this path can be made clear. In this chapter, the consequences of the BCM theory are explored in...