Van der Pol Oscillator

continuous-flows · 37 views
continuous-flowsperiodic

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 additionally detects Persistent Homology:max_h1_lifetime.

What standard analysis sees
tail heaviness0.05
asymmetry0.36
occupancy0.67
short-range corr0.97
long-range memory0.99
spectral colour0.22
periodicity0.89
complexity0.04
time-irreversibility0.81
volatility clustering0.92
multifractality0.78
dimensionality0.05
nonstationarity0.50
What the atlas adds
Persistent Homology:max_h1_lifetime+4.7z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Atlas-extreme metrics the standard bank can’t predict for this source
G2 Root System:short_long_ratio-3.8zbank-miss 2.4σ
Fisher Information:geodesic_velocity+2.4zbank-miss 1.7σ
Chladni:nodal_gap_ratio+2.3zbank-miss 1.0σ

Composition

dtypefloat64
range[-2.066, 2.066]
unique values16384 / 16384
mean ± std0.0297 ± 1.62

Render Gallery

Native > phase_plot
Native > phase_plotraw
Native > timeseries
Native > timeseriesraw
Native > triple_lattice
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > lag_map
Boltzmann > spin_grid
Boltzmann > spin_grid
Cayley > default
Cayley > default
Chladni > free_plate_nodal
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_bottom
Chladni > plate_top
Chladni > plate_top
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > xy_path
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
Hodge–Laplacian > default
Inflation (Substitution) > barcode
Inflation (Substitution) > barcode
Inflation (Substitution) > d_curve
Inflation (Substitution) > d_curve
Information Theory > default
Information Theory > default
Julia Set > escape_histogram
Julia Set > escape_histogram
Klein Bottle > default
Klein Bottle > default
Laplacian > default
Laplacian > default
Logarithmic Spiral > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Möbius-S³ > s2_base_map
Ordinal Partition > default
Ordinal Partition > default
Penrose (Quasicrystal) > phi_spectrum
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > barcode
Persistent Homology > h1_diagram
Persistent Homology > h1_diagram
Predictability > default
Predictability > default
Recurrence Quantification > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Analysis > default
Spectral Graph > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > flux_grid
Symplectic > phase_space
Symplectic > phase_space
Ulam Spiral (Sacks) > default
Ulam Spiral (Sacks) > default
Ulam Spiral (Square) > default
Ulam Spiral (Square) > default
Visibility Graph > default
Visibility Graph > default
Wavelet Cascade > default
Wavelet Cascade > default

Atlas Position

Nearest neighborDistance
Period-Doubled Wave3.74cross-origin
Duffing Oscillator3.74
Magnetic Pendulum (3-Magnet)3.90

Open in Atlas →

Which Geometries Light Up

2-adic › 2-adic:mean_distancerank 4/3060.6682
Catch24 › Catch24:FC_LocalSimple_mean1_tauresratrank 1/3061.0084
D4 Triality › D4 Triality:edge_ortho_polarityrank 5/3060.7382
D4 Triality › D4 Triality:gram_consistencyrank 302/3060.4575
E8 Lattice › E8 Lattice:std_profilerank 302/3060.1635
Fisher Information › Fisher Information:velocity_spectral_ginirank 2/3060.7915
G2 Root System › G2 Root System:short_long_ratiorank 306/3060.0662
Laplacian › Laplacian:gradient_sign_persistencerank 1/3060.9986
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_meanrank 4/3060.1353
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_stdrank 4/3060.1483
Möbius-S³ › Möbius-S³:hopf_fiber_coherencerank 5/3060.8023
Predictability › Predictability:sample_entropyrank 302/3060.0302
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_burstinessrank 5/3060.5923
Symplectic › Symplectic:flux_sign_persistencerank 1/306345.3302
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropyrank 1/3060.0454
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergencerank 3/3060.9955
Visibility Graph › Visibility Graph:degree_r_squaredrank 304/3060.2299
p-Variation › p-Variation:variation_indexrank 304/3061.0005
in iterated-maps(last) →
alphabetical
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources

Structure Atlas — Open Atlas · GitHub