Random iterative networks
Paul C. Bressloff, John G. Taylor · Physical Review A · 1990
A general framework for introducing noise into binary networks is developed using random iterative maps. The dynamics of these random iterative networks is written in terms of Markov chains and notions of ergodicity discussed. Generic features of the statistical dynamics of such networks are explored and a path-integral formulation of macroscopic dynamics derived. Two examples are used for illustration. First, the Little model is shown to be equivalent to a random iterative network with threshold noise, and this is used to derive the mean-field equations for a network with random dilution. Second, mean-field equations are derived for networks with synaptic noise, whose form depends crucially on how the thermodynamic limit is defined.