Adiabatic Elimination — Fast-Slow Manifold & Slow Manifold Reduction

System: ẋ=f(x,y), εẏ=g(x,y). As ε→0, fast variable y slaved to slow x via g(x,y)=0. Trajectories collapse onto the slow manifold. Demonstrates center manifold reduction.

ε (timescale sep.): 0.10 α (coupling): 1.0 IC x₀: 1.5

ε→0: fast y collapses to slow manifold g(x,y)=0