A stochastic model for interconnected neurons

A model is proposed to describe the collective behavior of a biologically plausible neural network, composed of interconnected spiking neurons which separately receive external stationary stimulations. The spiking dynamics of each neuron is represented by an hourglass metaphor. This network model was first studied in a special case where the connections 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 case), the system is ergodic and all neurons have a positive mean firing rate. In the other states (divergent case), some neurons become definitively inactive while the sub-network of the active neurons is ergodic. The patterns which result from these divergent states can be seen as a neural coding of the external stimulation by the network. This property is applied to the olfactory system to produce a code for an odor. The role of inhibitory connections in odor discrimination is studied.