Correlations and Memory in Neurodynamical Systems

The operation of the nervous system relies in great part on the firing activity of neurons. This activity exhibit significant fluctuations on a variety of time scales as well as a number of memory effects. We discuss examples of stochastic and memory effects that have arisen in our neuronal modeling work on a variety of systems. The time scales of these effects range from milliseconds to seconds. Our discussion focusses on 1) the effect of long-range correlated noise on signal detection in neurons, 2) the correlations and multistability produced by propagation delays, and 3) the long time scale “working memory” effects seen in cortex, and their interaction with intrinsic neuronal noise. We describe both analytical and numerical approaches. We further highlight the challenges of constraining theoretical analyses with experimental data, and of attributing functional significance to correlations produced by noise and memory effects.