Propagation of Spike Sequences in Neural Networks

Precise spatiotemporal sequences of action potentials are observed in many brain areas and are thought to be involved in the neural processing of sensory stimuli. Here, we examine the ability of spiking neural networks to propagate stably a spatiotemporal sequence of spikes in the limit where each neuron fires only one spike. In contrast to previous studies on propagation in neural networks, we assume only homogeneous connectivity and do not use the continuum approximation. When the propagation is associated with a simple traveling wave, or a one-spike sequence, we derive some analytical results for the wave speed and show that its stability is determined by the Schur criterion. The propagation of a sequence of several spikes corresponds to the existence of stable composite waves, i.e., stable spatiotemporal periodic traveling waves. The stability of composite waves is related to the roots of a system of multivariate polynomials. Using the simplest synaptic architecture that supports composite waves, a three nearest-neighbor coupling feedforward network, we analytically and numerically investigate the propagation of 2-composite waves, i.e., two-spike sequence propagation. The influence of the synaptic coupling, stochastic perturbations, and neuron parameters on the propagation of larger sequences is also investigated.