Speed-Up Methods for Simulations of Traveling Waves in Large-Scale Integrate-and-Fire Neural Networks

We consider single and multiple spike traveling waves solutions in an integrate-and-fire neural network. Due to the special properties of this system it is possible to deduce the dynamical state of each neuron in the full network from a small subset, using recurrence relationships. Since the dimension of the subset is equal to the number of the traveling waves, this greatly reduces the computational time required for numerical simulations. These ideas are specific to the class of integrate-and-fire neural network models presented here.