NOS with event-based coupling, topology control, and the operator margin g⋆ ≈ k⋆/ρ(W).
v (queue proxy)u (recovery)external arrivalsincoming network spikesoutput spike
Phase plane: v vs u (focus node)
Mascot: queue mood & packet bursts
Operator margin (topology → gain budget)
ρ(W)raw = –, ρ(W)used = –
k⋆ (local bound, no delay) = –
g⋆ ≈ k⋆/ρ(W)raw = – (paper-style)
Current: g = – ⇒ k = g·ρ(W)sim = –
Status: compute W(surrogate margin, not a hybrid reset proof)
NOS drift: dv = f_sat(v) + (β − λ)v − u + I_ext + I_net, du = a(bv − u) (here μ=χ=γ=0).
Event at v_new ≥ θ with pullback reset v ← c + (v−c)e^{−ρ_reset Δt} and recovery kick u ← u + Δu.
Coupling is event-based: I_net,i(t) = g·∑_j W_{ij} S_j(t−τ_{ij}). Simulation uses W_used for W.
What to look for
If you raise the topology spectral radius ρ(W) (dense hub, scale-free), the gain budget g⋆ ≈ k⋆/ρ(W) shrinks.
If you keep g fixed and change topology, you should see transitions into oscillatory or bursty spiking, with v repeatedly hitting θ and u lagging.
Normalising to ρ(W)=1 makes topologies comparable under the same g in simulation, while still reporting the raw ρ(W) for the margin formula.
All coupling in this demo is event-based (spikes), never “coupling through nonlinearity”.