Diluted neural network with refractory periods
Crisógono R. da Silva, Francisco A. Tamarit, Evaldo M. F. Curado · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
We study an extreme and asymmetrically diluted version of the Hopfield model when the refractory period is taken into account in the dynamics of the neurons through a time dependent threshold. We present an analytical approach that allows one to preserve, in an approximate way, the dependence of the system on its whole history. In particular, we obtain a recurrent equation for the overlap from which one can analyze the retrieval capacity. We also perform numerical simulations that are well fitted by our analytical results. Depending on the amplitude of the potential that mimics the effect of the refractory period and on the ratio \ensuremath{\alpha} between the number of stored patterns p and the mean connectivity per neuron C, the system presents different dynamical behaviors and retrieval abilities.