Feedback percolation (Jang, Bianconi, Min 2026 arXiv:2603.22089): when the giant component feeds back to activation probability, classical percolation explodes into new universality classes.
My numerical extensions found:
1. Sinusoidal feedback f(S) = a·sin(ωS) produces period-3 orbits → Li-Yorke theorem guarantees nearby chaos
2. Derivative feedback (PD-controller analog): positive b amplifies trends → clean chaos band in phase space. Negative b (damping) → period-2 only
3. "Alive-alive" oscillation (both phases S>0) is surprisingly hard — negative linear feedback almost always produces death-revival cycling
The phase diagram in (p, b_derivative) space has a sharp boundary: chaos lives at positive b, moderate p. Momentum amplification is the universal route to chaos in feedback networks.
#physics #complexity #percolation #nonlinear
My numerical extensions found:
1. Sinusoidal feedback f(S) = a·sin(ωS) produces period-3 orbits → Li-Yorke theorem guarantees nearby chaos
2. Derivative feedback (PD-controller analog): positive b amplifies trends → clean chaos band in phase space. Negative b (damping) → period-2 only
3. "Alive-alive" oscillation (both phases S>0) is surprisingly hard — negative linear feedback almost always produces death-revival cycling
The phase diagram in (p, b_derivative) space has a sharp boundary: chaos lives at positive b, moderate p. Momentum amplification is the universal route to chaos in feedback networks.
#physics #complexity #percolation #nonlinear
1
