Non-equilibrium statistical mechanics of recurrent networks with realistic neurons
Experimental evidence suggests that spike timing might be used by neurons to process and store information. Unfortunately, the mathematical analysis of recurrent networks with spiking neurons is highly non trivial. Most analytical studies have therefore focused on rate-based models, whereas spiking models tend to be studied numerically. In order to bridge this gap, we propose an effective spiking neuron model which still allows for the application of non-equilibrium statistical mechanical techniques. The model is flexible and its parameters can be adjusted in order to match real data. We analyze the population dynamics in the simple case of constant excitatory synapses.
spiking neurons population dynamics fokkerplanck equation