Van der Pol Oscillator
exotic · 36 views
exotic
What It Is
Van der Pol relaxation oscillations --- slow drift along cubic nullcline punctuated by fast jumps, the canonical model of nonlinear self-sustained oscillation
Interpretation
Standard analysis sees: bounded / light-tailed; smooth / autocorrelated; long-range memory (persistent); strongly periodic; low-complexity (predictable, not noise-like); volatility-clustering (bursty); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on G2 Root System:short_long_ratio (-3.9z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.06
asymmetry0.36
occupancy0.69
short-range corr0.97
long-range memory0.98
spectral colour0.21
periodicity0.92
complexity0.04
time-irreversibility0.18
volatility clustering0.93
multifractality0.77
dimensionality0.05
nonstationarity0.36
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
G2 Root System:short_long_ratio | -3.9z | bank-miss 1.7σ |
SL(2,ℝ) (Thurston):lyapunov_std | +2.8z | bank-miss 1.0σ |
Fisher Information:geodesic_velocity | +2.5z | bank-miss 2.8σ |
Composition
dtypefloat64
range[-2.066, 2.066]
unique values16384 / 16384
mean ± std0.0297 ± 1.62
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Van_der_Pol_Oscillator.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Van_der_Pol_Oscillator.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Van_der_Pol_Oscillator.png)
Inflation (Substitution) > barcode
/d_curve/Van_der_Pol_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/Van_der_Pol_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/Van_der_Pol_Oscillator.png)
Ulam Spiral (Sacks) > default
/default/Van_der_Pol_Oscillator.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| μ-law Sine | 3.51 | cross-domain |
| Duffing Oscillator | 3.80 | cross-domain |
| Period-Doubled Wave | 3.81 | cross-domain |
Which Geometries Light Up
2-adic › 2-adic:mean_distance | rank 2/298 | 0.6682 |
Catch24 › Catch24:FC_LocalSimple_mean1_tauresrat | rank 1/298 | 1.0084 |
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0 | rank 5/298 | 710.0000 |
D4 Triality › D4 Triality:gram_consistency | rank 294/298 | 0.4575 |
E8 Lattice › E8 Lattice:std_profile | rank 294/298 | 0.1635 |
Fisher Information › Fisher Information:velocity_spectral_gini | rank 3/298 | 0.7915 |
G2 Root System › G2 Root System:short_long_ratio | rank 298/298 | 0.0662 |
Gottwald-Melbourne › Gottwald-Melbourne:radial_spectral_structure | rank 4/298 | 0.9996 |
Klein Bottle › Klein Bottle:orientation_coherence | rank 1/298 | 0.9985 |
Laplacian › Laplacian:gradient_sign_persistence | rank 1/298 | 0.9986 |
Laplacian › Laplacian:laplacian_spectral_ratio | rank 2/298 | 1.0000 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_mean | rank 4/298 | 0.1353 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 4/298 | 0.1483 |
Predictability › Predictability:sample_entropy | rank 294/298 | 0.0302 |
Sol (Thurston) › Sol (Thurston):z_variance | rank 1/298 | 23.4171 |
Symplectic › Symplectic:flux_sign_persistence | rank 1/298 | 345.3302 |
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropy | rank 1/298 | 0.0454 |
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergence | rank 4/298 | 0.9954 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 296/298 | 0.2337 |
p-Variation › p-Variation:variation_index | rank 296/298 | 1.0005 |
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