Synchronization on the random graph with non-linear interaction: application to breathing.

We consider a system of leaky integrate-and-fire neurons interacting through a lognormal distribution of synaptic weights on random, directed graphs. This system is a good approximation of the preBötzinger Complex, the central pattern generator that sets the inspiratory rhythm in mammals by periodic bursting. We validate the model by comparing its prediction with the results of external burst initiation by the stimulation of a small subset of neurons in the preBötzinger Complex, which leads to synchronized spiking in the network that preceeds the burst of inspiratory activity. Comparing the probability of a burst and the time delay between that stimulation and the burst as the function of number of stimulated neurons, we obtain the quantitative fit to the experimental data with no free parameters. We then explore the process of the burst initiation in this model by asking the question: what features of the network and the stimulated neurons determine whether the burst will occur or not? Using the graph theory and a simplified version of the model, we suggest a list of quantities that we expect to be good predictors of the burst and evaluate the performance of these quantities using machine learning.