Critical Slowing Down Governs the Transition to Neuron Spiking
Fig 2
Illustration of stochastic scaling laws near the saddle-node (fold) bifurcation in a model system.
a, Phase space with a single stochastic sample path (black) of a saddle-node bifurcation (eq. 10) for the initial condition (V(0), y(0)) = (−4, 1.6) with σ1 = 0.001, ϵ = 0.001 and small perturbations of size σ2(ti) = 0.1 with ti = 60. The bifurcation occurs at (Vc, yc) = (0, 0) (red dot). The gray curves are the system equilibria (for ϵ = 0). b, Sample path Vd plotted as a time series where the equilibrium values have been subtracted (i.e. detrending along the equilibrium branch). c, Scaling of recovery rate λ, variance v and autocorrelation as dynamics approaches the bifurcation point (red vertical line). Recovery rate and variance follow a power-law scaling with exponents ±0.5 illustrated by black dashed lines.