Critical Slowing Down Governs the Transition to Neuron Spiking
Fig 3
Illustration of stochastic scaling laws near the subcritical Hopf bifurcation in a model system.
a, Phase space with a single stochastic sample path (black) of a Hopf bifurcation (eq. 12) for the initial condition (V1(0), V2(0), y0) = (0, 0, −2) with σ1, 2 = 0.001, ϵ = 0.001 and small perturbations of size σ3(ti) = 0.005 with ti = 60. The bifurcation occurs at (V1c, V2c, yc) = (0, 0, 0) (red dot). b, Sample path V1 plotted as a time series used for further analysis. 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 ±1 illustrated by black dashed lines.