Self Tuned Criticality: Controlling a neuron near its bifurcation point via temporal correlations

TL;DR

This paper demonstrates that a single neuron can be self-tuned to its bifurcation point using a control method based on temporal correlations, extending previous network-level control to low-dimensional systems.

Contribution

It introduces a novel control approach that uses autocorrelation to tune a neuron near its bifurcation point, applicable to simple models like FitzHugh-Nagumo.

Findings

Neuron dynamics can be controlled near bifurcation points.

Control method works for both excitable maps and FitzHugh-Nagumo models.

Autocorrelation coefficient guides the self-tuning process.

Abstract

Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such correlations behave similarly near instabilities across nonlinear dynamical systems, it is expected that the principle should control also low dimensional dynamical systems exhibiting continuous or discontinuous bifurcations from fixed points to limit cycles. Here we present numerical evidence that the dynamics of a single neuron can be controlled in the vicinity of its bifurcation point. The approach is tested in two models: a 2D generic excitable map and the paradigmatic FitzHugh-Nagumo neuron model. The results show that in both cases, the system can be self-tuned to its bifurcation point by modifying the control parameter according to the first coefficient of the autocorrelation function.