Chaos Metrics

Examples illustrating the quantitative chaos-diagnostic tools in physicskit.chaos.utils and their companion visualizers: trajectory-divergence-based and QR (Benettin)-based Lyapunov exponent estimation, integrator energy drift, phase-space volume contraction, Poincare recurrence / Kac’s lemma, fractal (box-counting and correlation) dimension estimation, bifurcation diagrams for periodically-forced continuous flows (see Logistic Map: the Period-Doubling Route to Chaos for the discrete-map case), and Pomeau-Manneville intermittency near a tangent bifurcation.

Bifurcation Diagrams for Continuous Flows: the Duffing Oscillator

Bifurcation Diagrams for Continuous Flows: the Duffing Oscillator

Energy Drift vs. Integration Step Size

Energy Drift vs. Integration Step Size

Fractal Dimension: Box-Counting and Correlation Dimension

Fractal Dimension: Box-Counting and Correlation Dimension

Pomeau-Manneville intermittency: laminar phases and chaotic bursts

Pomeau-Manneville intermittency: laminar phases and chaotic bursts

Lyapunov Divergence: Chaotic vs. Non-Chaotic

Lyapunov Divergence: Chaotic vs. Non-Chaotic

Full Lyapunov Spectrum (Benettin QR Method)

Full Lyapunov Spectrum (Benettin QR Method)

Phase-Space Volume Contraction (Liouville’s Theorem)

Phase-Space Volume Contraction (Liouville's Theorem)

Poincare Recurrence and Kac’s Lemma

Poincare Recurrence and Kac's Lemma

Analyzing a Raw Time Series (No Equations Required)

Analyzing a Raw Time Series (No Equations Required)