Duffing Oscillator
continuous-flows · 37 views
continuous-flowschaotic
What It Is
Driven damped nonlinear oscillator --- strange attractor with broad amplitude visits
Interpretation
Standard analysis sees: rich, high-entropy values; smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); volatility-clustering (bursty). The atlas additionally detects Nonstationarity:adf_pvalue, Multifractal Spectrum:hurst_estimate. It sits beside Hénon-Heiles in the atlas (standard-bank rank 56) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.32
asymmetry0.27
occupancy0.89
short-range corr0.96
long-range memory0.90
spectral colour0.13
periodicity0.57
complexity0.08
time-irreversibility0.20
volatility clustering0.96
multifractality0.80
dimensionality0.23
nonstationarity0.60
What the atlas adds
Nonstationarity:adf_pvalue+3.5z
unit-root nonstationarity (ADF cannot reject random-walk null)
Multifractal Spectrum:hurst_estimate+2.5z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
Chladni:modal_nodal_cascade | -4.3z | bank-miss 1.1σ |
Laplacian:curvature_autocorrelation | +2.0z | bank-miss 1.5σ |
Composition
dtypefloat64
range[-1.483, 1.497]
unique values16384 / 16384
mean ± std-0.0356 ± 0.86
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Duffing_Oscillator.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Duffing_Oscillator.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Duffing_Oscillator.png)
Inflation (Substitution) > barcode
/d_curve/Duffing_Oscillator.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Duffing_Oscillator.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Duffing_Oscillator.png)
Ulam Spiral (Sacks) > default
/default/Duffing_Oscillator.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Chua's Circuit | 2.35 | |
| Hénon-Heiles | 2.88 | |
| FPUT N=16 | 2.91 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:CO_HistogramAMI_even_2_5 | rank 4/307 | 1.4607 |
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiff | rank 5/307 | 30.6658 |
Chladni › Chladni:modal_nodal_cascade | rank 306/307 | -0.5824 |
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 5/307 | 5.5737 |
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 5/307 | 0.9986 |
Laplacian › Laplacian:curvature_autocorrelation | rank 5/307 | 0.9986 |
Laplacian › Laplacian:biharmonic_ratio | rank 303/307 | 0.0000 |
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropy | rank 4/307 | 0.0393 |
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