Tool

Lyapunov from time series

Rosenstein's algorithm: time-delay embed your data, track the mean log distance between nearest-neighbour trajectories, and fit a slope. Drag-drop a CSV with one numeric column.

source: logistic-r4 (sample) · samples used: 1,500

m (embed dim): 3

τ (delay): 1

Theiler window: 10

Max k: 40

Rosenstein largest-Lyapunov

1. Time-delay embed: y_i = (x_i, x_{i+τ}, ..., x_{i+(m−1)τ})
2. For each y_i, find nearest neighbour y_j (|i − j| > Theiler window)
3. Track mean separation d_k = ⟨ log |y_{i+k} − y_{j+k}| ⟩
4. Slope of d_k vs k ≈ largest Lyapunov exponent.

Estimated λ₁ ≈ 0.1573
Verdict: CHAOTIC (λ₁ > 0)

Drop a CSV with one numeric column to analyse your own data.

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