Bump attractors and waves in networks of leaky integrate-and-fire neurons
Avitabile, D; Davis, JL; Wedgwood, KC
Date: 9 February 2023
Article
Journal
SIAM Review
Publisher
Society for Industrial and Applied Mathematics
Publisher DOI
Abstract
Bump attractors are wandering localised patterns observed in in vivo experiments
of spatially-extended neurobiological networks. They are important for the brain’s navigational
system and specific memory tasks. A bump attractor is characterised by a core in which neurons
fire frequently, while those away from the core do not fire. ...
Bump attractors are wandering localised patterns observed in in vivo experiments
of spatially-extended neurobiological networks. They are important for the brain’s navigational
system and specific memory tasks. A bump attractor is characterised by a core in which neurons
fire frequently, while those away from the core do not fire. These structures have been found in
simulations of spiking neural networks, but we do not yet have a mathematical understanding of their
existence because a rigorous analysis of the nonsmooth networks that support them is challenging.
We uncover a relationship between bump attractors and travelling waves in a classical network of
excitable, leaky integrate-and-fire neurons. This relationship bears strong similarities to the one
between complex spatiotemporal patterns and waves at the onset of pipe turbulence. Waves in the
spiking network are determined by a firing set, that is, the collection of times at which neurons
reach a threshold and fire as the wave propagates. We define and study analytical properties of the
voltage mapping, an operator transforming a solution’s firing set into its spatiotemporal profile. This
operator allows us to construct localised travelling waves with an arbitrary number of spikes at the
core, and to study their linear stability. A homogeneous “laminar” state exists in the network, and
it is linearly stable for all values of the principal control parameter. Sufficiently wide disturbances
to the homogeneous state elicit the bump attractor. We show that one can construct waves with a
seemingly arbitrary number of spikes at the core; the higher the number of spikes, the slower the
wave, and the more its profile resembles a stationary bump. As in the fluid-dynamical analogy,
such waves coexist with the homogeneous state, and the solution branches to which they belong are
disconnected from the laminar state; we provide evidence that the dynamics of the bump attractor
displays echoes of unstable waves, which form its building blocks.
Mathematics and Statistics
Faculty of Environment, Science and Economy
Item views 0
Full item downloads 0