Dr. Louis Tao published a paper on Physical Review E with his collaborator.
Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. Because of their neutral stability along a linear manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. In this paper, we make the connection between line attractors and pulse-gating in feedforward neuronal networks. To understand how pulse-gating manifests itself in a high dimensional, non-linear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze the dynamics of the system. After making a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, we identify an approximate line attractor in state space as the essential structure underlying graded information propagation in our solutions. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the linear manifold defined by the fixed points, the dynamics are slow giving rise to ghost dynamics. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and thus, dynamically control the processing of graded information.
Original link: https://link.aps.org/doi/10.1103/PhysRevE.96.052308
