Lotka-Volterra
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bio
What It Is
Predator-prey oscillations --- nonlinear limit cycles with phase-shifted population waves
Interpretation
Standard analysis sees: smooth / autocorrelated; low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); volatility-clustering (bursty); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on Visibility Graph:degree_exponent_gamma (-2.9z) — beyond what the standard bank predicts for it. It sits beside Duffing Oscillator in the atlas (standard-bank rank 24) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.46
asymmetry0.81
occupancy0.59
short-range corr0.92
long-range memory0.83
spectral colour0.20
periodicity0.80
complexity0.05
time-irreversibility0.04
volatility clustering0.91
multifractality0.82
dimensionality0.04
nonstationarity0.45
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Visibility Graph:degree_exponent_gamma | -2.9z | bank-miss 1.3σ |
Bispectrum:coupling_frequency_centroid | -2.6z | bank-miss 1.7σ |
Composition
dtypefloat64
range[2.023, 3.8]
unique values16384 / 16384
mean ± std2.82 ± 0.626
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/Lotka-Volterra.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Lotka-Volterra.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Lotka-Volterra.png)
Inflation (Substitution) > barcode
/d_curve/Lotka-Volterra.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/Lotka-Volterra.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/Lotka-Volterra.png)
Ulam Spiral (Sacks) > default
/default/Lotka-Volterra.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Rossler Attractor | 3.40 | cross-domain |
| Damped Pendulum | 3.42 | cross-domain |
| Duffing Oscillator | 3.54 | cross-domain |
Which Geometries Light Up
Chladni › Chladni:modal_nodal_cascade | rank 295/298 | -0.4789 |
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 1/298 | 5.3673 |
Laplacian › Laplacian:laplacian_spectral_ratio | rank 3/298 | 1.0000 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 3/298 | 0.8566 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 297/298 | 0.2289 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources