ix-chaos

name	ix-chaos
description	Chaos theory analysis — Lyapunov exponents, bifurcation, attractors, fractals
disable-model-invocation	true

Chaos Analysis

Analyze dynamical systems and time series for chaotic behavior.

When to Use

When the user has time series data that might be chaotic, wants to study dynamical systems, or needs fractal dimension estimates.

Capabilities

• Lyapunov exponents — Positive = chaos, zero = periodic, negative = stable
• Bifurcation diagrams — How system behavior changes with a parameter
• Strange attractors — Lorenz, Rössler, Chen system integration
• Fractal dimensions — Box-counting, correlation dimension, Hurst exponent
• Delay embedding — Reconstruct attractor from scalar time series (Takens' theorem)
• Poincaré sections — Reduce continuous dynamics to discrete maps
• Chaos control — OGY method, Pyragas time-delay feedback

Programmatic Usage

use ix_chaos::lyapunov::{mle_1d, classify_dynamics};
use ix_chaos::bifurcation::bifurcation_diagram;
use ix_chaos::attractors::{lorenz, integrate};
use ix_chaos::fractal::box_counting_dimension_2d;
use ix_chaos::embedding::{delay_embed, optimal_delay};

Quick Check

For the logistic map x_{n+1} = r * x_n * (1 - x_n):

• r < 3.0: stable fixed point
• r ≈ 3.57: onset of chaos
• r = 4.0: fully chaotic