NOS topology–margin demo

This demo visualises the local linear surrogate from your NOS appendix code: build the 2N×2N block Jacobian with A11 = d̄ I + k W_eff, A12 = −I, A21 = (ab)I, A22 = −(a+μ)I, where d̄ = f′(v*) + (β − λ − χ). For symmetric nonnegative W, the critical coupling scales like k* ∝ 1/ρ(W_eff).

Controls

Selected topology (highlight & regenerate)

N (nodes)

120

Mean degree / k

Weight model

Random seed

Symmetrise W

Keeps eigenvalues real so the 2×2 mode reduction is exact.

Normalise to ρ(W)=1

Useful to show that k*ρ stays constant.

Coupling gain k

k = 0.250

NOS operating point + parameters

These map to the surrogate in linearisation.py. They do not run a spiking simulation.

v* (operating point)

0.200

α (saturation)

0.000

κ (saturation)

0.000

λ (leak)

0.600

0.000

1.000

0.800

0.500

Use coupling through nonlinearity (deprecated) Plot x-axis as ρ(W_eff) (moves points when enabled)

Tip: the k slider draws a horizontal line on the plot, so you can see whether k sits below k* for each topology.

If enabled, the demo uses W_eff = f′(v*) W. Your public code deprecates this for the paper.

ρ(W) (raw)

–

ρ(W_eff)

–

f′(v*)

–

d̄ = f′ + (β − λ − χ)

–

k* (det bound)

–

k* (trace bound)

–

k* (active)

–

k ρ(W_eff)

–

Status

–

Plot: k* vs ρ(W)

The straight line corresponds to k* = C / ρ(W_eff) with C = min(a b/(a+μ) − d̄, (a+μ) − d̄). This follows the symmetric-W block-Jacobian surrogate. It is a local condition around v*.