Slow Manifold & Center Manifold Reduction

Fast-slow system: the fast variable y collapses quickly onto the slow manifold y ≈ h(x). Trajectories first rush to the manifold (fast transient), then follow slow reduced dynamics along it.

ẋ = x − x³ − y | εẏ = −y + x² (slow manifold: y* = x²)

Time-scale ε: 0.10

Nonlinearity α: 1.0

N trajectories: 12