How Transmission Delays and Noise Modify the Simple and Large Neural Networks Dynamics

Abstract

In the nervous system, information transfer is partly mediated by action potentials travelling along axons connecting neurons. Conduction velocity ranges from 20 to 60 m/s, leading to non negligible transmission delays, from milliseconds to hundreds of milliseconds. These delays, referred to as inter-neural delays (INDs) reflect axonal propagation time, synaptic delay, etc., can greatly affect the behavior of living neural networks. The effect of IND on the dynamics of a single neuron receiving recurrent excitation after a controlled delay, and on those of large fully interconnected excitatory networks were described and analyzed in two previous papers (Pakdaman et al., 1996; Vibert et al.. 1996). Noise, as INDs, is also omnipresent in the nervous system, and can greatly modify the behavior of neurons and neural networks (Segundo et al., 1994). In this paper, we are interested on how noise affects the IND effect on both the single neuron with recurrent excitation and the excitatory neural network.