Individual skill
dynamical-systems
Analyze nonlinear dynamical systems — phase portraits, fixed points, stability analysis, bifurcation diagrams, Poincare sections, Lyapunov exponents, and chaos detection. Use for any autonomous or non-autonomous ODE system where qualitative behavior matters.
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# Dynamical Systems Analysis
## Overview
Qualitative and quantitative analysis of nonlinear dynamical systems. Phase portraits, fixed point classification, stability analysis, bifurcation diagrams, Poincare sections, and Lyapunov exponent computation.
## When to Use
- Visualizing flow in phase space (2D and 3D systems)
- Finding and classifying fixed points (stable/unstable nodes, spirals, saddles, centers)
- Bifurcation analysis (how qualitative behavior changes with parameters)
- Detecting chaos (Lyapunov exponents, sensitivity to initial conditions)
- Poincare sections for periodicity analysis
- Limit cycle detection and characterization