A STOCHASTIC-MODEL FOR INTERCONNECTED NEURONS

A model is proposed to describe the collective behavior of a biologica lly plausible neural network, composed of interconnected spiking neuro ns which separately receive external stationary stimulations. The spik ing dynamics of each neuron is represented by an hourglass metaphor. T his network model was first studied in a special case where the connec tions are only inhibitory (Cottrell, 1988, 1992). We study the network dynamics as a function of the parameters which quantify the strengths of both inhibitory and excitatory connections. We show that the model exhibits two kinds of limit states. In the first states (convergent c ase), the system is ergodic and all neurons have a positive mean firin g rate. In the other states (divergent case), some neurons become defi nitively inactive while the sub-network of the active neurons is ergod ic. The patterns which result from these divergent states can be seen as a neural coding of the external stimulation by the network. This pr operty is applied to the olfactory system to produce a code for an odo r. The role of inhibitory connections in odor discrimination is studie d.