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; red spectrum (low-frequency / 1-over-f power); strongly periodic; 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.
What standard analysis sees
tail heaviness0.26
asymmetry0.74
occupancy0.72
short-range corr0.91
long-range memory0.81
spectral colour0.08
periodicity0.96
complexity0.07
time-irreversibility0.07
volatility clustering0.88
multifractality0.76
dimensionality0.09
nonstationarity0.34
What the atlas adds
Persistent Homology:max_h1_lifetime+4.9z
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
Visibility Graph:degree_exponent_gamma | -3.0z | bank-miss 1.5σ |
Hodge–Laplacian:poisson_recovery_error | +2.9z | bank-miss 1.0σ |
Bispectrum:coupling_frequency_centroid | -2.6z | bank-miss 1.7σ |
Visibility Graph:assortativity | +2.2z | bank-miss 1.1σ |
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 | 3.38 | |
| Damped Pendulum | 3.40 | |
| Sine Wave | 3.53 | cross-origin |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_residual_frac | rank 302/306 | 0.0000 |
Chladni › Chladni:modal_nodal_cascade | rank 303/306 | -0.4789 |
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 1/306 | 5.3673 |
Persistent Homology › Persistent Homology:max_h1_lifetime | rank 5/306 | 0.7349 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 3/306 | 0.8566 |
Visibility Graph › Visibility Graph:assortativity | rank 4/306 | 0.5383 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 302/306 | 0.2995 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 305/306 | 0.2289 |
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