Dynamic Mode Decomposition — spectral analysis of nonlinear dynamics
System
Parameter μ1.00
DMD rank r4
Delay τ3
Koopman operator K acts on observables g: (Kg)(x) = g(F(x)) — lifts nonlinear dynamics to an infinite-dimensional linear operator. DMD approximates the leading Koopman eigenvalues λ_k and modes φ_k from data snapshots: x(t+1) ≈ A·x(t), A ≈ Φ·Λ·Φ⁻¹.
Eigenvalues on the unit circle → stable oscillations. Inside → decaying. DMD modes reveal coherent spatiotemporal structures. Delay embedding (Hankel DMD) enriches observable space to better approximate Koopman eigenfunctions.