Stable and Unstable Periodic Orbits in Complex Networks of Spiking Neurons with Delays

@inproceedings{Memmesheimer2010StableAU,
title={Stable and Unstable Periodic Orbits in Complex Networks of Spiking Neurons with Delays},
author={Raoul-Martin Memmesheimer},
year={2010}
}

Is a periodic orbit underlying a periodic pattern of spikes in a heterogeneous neural network stable or unstable? We analytically assess this question in neural networks with delayed interactions by explicitly studying the microscopic time evolution of perturbations. We show that in purely inhibitorily coupled networks of neurons with normal dissipation (concave rise function), such as common leaky integrate-and-fire neurons, all orbits underlying non-degenerate periodic spike patterns are… CONTINUE READING