Lotka-Volterra
continuous-flows · 37 views
continuous-flowsperiodic
What It Is
Predator-prey oscillations --- conservative nonlinear cycles (a continuum of nested closed orbits about a center, not an isolated limit cycle) 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 additionally detects Persistent Homology:max_h1_lifetime, Multi-Scale Wasserstein:w_max_ratio.
What standard analysis sees
tail heaviness0.46
asymmetry0.81
occupancy0.59
short-range corr0.91
long-range memory0.83
spectral colour0.20
periodicity0.80
complexity0.05
time-irreversibility0.04
volatility clustering0.91
multifractality0.82
dimensionality0.04
nonstationarity0.44
What the atlas adds
Persistent Homology:max_h1_lifetime+4.8z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Multi-Scale Wasserstein:w_max_ratio+2.1z
scale-coherent dispersion mismatch (max/min Wasserstein across scales)
Atlas-extreme metrics the standard bank can’t predict for this source
Visibility Graph:degree_exponent_gamma | -3.0z | bank-miss 1.2σ |
Hodge–Laplacian:poisson_recovery_error | +2.9z | bank-miss 1.1σ |
Bispectrum:coupling_frequency_centroid | -2.6z | bank-miss 1.8σ |
Visibility Graph:assortativity | +2.2z | bank-miss 1.3σ |
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 > free_plate_nodal
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 | 3.37 | |
| Damped Pendulum | 3.41 | |
| Sine Wave | 3.54 | cross-origin |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_residual_frac | rank 303/307 | 0.0000 |
Chladni › Chladni:modal_nodal_cascade | rank 304/307 | -0.4789 |
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 1/307 | 5.3673 |
Persistent Homology › Persistent Homology:max_h1_lifetime | rank 5/307 | 0.7349 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 3/307 | 0.8566 |
Visibility Graph › Visibility Graph:assortativity | rank 4/307 | 0.5383 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 303/307 | 0.2995 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 306/307 | 0.2289 |
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