ANALYSIS OF QUANTAL SYNAPTIC NOISE IN NEURAL NETWORKS USING ITERATED FUNCTION SYSTEMS

It is shown how the dynamics of a discrete-time leaky-integrator (time-summating) neural network with quantal synaptic noise may be formulated in terms of a random iterated function system. Conditions are derived for which the limiting behavior of the system is described by an invariant probability measure on the space of membrane potentials. Such an invariant measure typically has a fractal-like structure, which is illustrated by a simple example of a single neuron with inhibitory feedback. The effects of synaptic noise on the response characteristics of the neuron are also considered. Finally, learning in networks with synaptic noise is discussed.