Weakly interacting pulses in synaptically coupled neural media

We use singular perturbation theory to analyze the dynamics of $N$ weakly interacting pulses in a one-dimensional, synaptically coupled neuronal network. The network is modeled in terms of a non-local integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights and the output activity of a neuron is taken to be a mean firing rate. We derive a set of $N$ coupled ordinary differential equations (ODEs) for the dynamics of individual pulses, establishing a direct relationship between the explicit form of the pulse interactions and the structure of the long-range synaptic coupling. The system of ODEs is used to explore the existence and stability of stationary $N$-pulses and traveling wave trains.


University of Utah | Department of Mathematics |
bressloff@math.utah.edu
Aug 2001.