Toolbox Chaos documentation
Tutorials, functions, and research workflows
Use the desktop GUI to define numerical experiments, simulate registered or custom dynamical systems, connect multiple visual and diagnostic views, explore parameters and initial conditions, and export traceable results. Each new workflow states its objective, exact tab, procedure, expected result, interpretation, applications, export record, and scientific limits.
Start here
4 guidesGetting Started
Install the desktop application, run a first catalog example, reuse its trajectory, and save a figure.
Interface Overview
Understand the 13 tabs, shared trajectory workflow, controls, status messages, and where each task belongs.
System Catalog
Choose among 38 registered flows, maps, delay and special models without confusing catalog status with a dynamical claim.
Concepts and Visual Theory of Chaos
Definitions, figures, and reading strategies for students entering chaotic systems for the first time.
Simulation and visualization
5 guidesLorenz Attractor Quick Start
Set parameters, run a first simulation, and compare 3D phase space with projected 2D portraits.
3D Attractor View
Configure a three-dimensional catalog simulation, inspect projections, and distinguish geometry from proof of attraction.
2D Phase Portraits
Select state-variable pairs, reuse a trajectory, and read folds, loops, crossings, and projection artifacts.
Time Series
Inspect state histories, transients, oscillations, bursts, drift, and numerical failure before deeper analysis.
Compare Integration Methods
Compare Euler, Heun, and RK4 under the same numerical contract and perform a practical step-size study.
Diagnostics and parameter exploration
8 guidesSpectral Analysis
Choose Welch PSD or an amplitude spectrum, discard transients, set frequency limits, and interpret units correctly.
FFT Example
A focused example for generating and reading the Lorenz amplitude spectrum.
Lyapunov Exponent Diagnostics
Visualize perturbation growth and read convergence-aware finite-time exponent estimates.
Bifurcation Diagrams
Configure parameter sweeps, retained points, Poincare sections, and Hopf examples.
Basins of Attraction
Read finite-resolution basin maps and representative trajectories launched from different regions.
Coexisting Attractors
Compare registered multistability cases under fixed parameters and distinct initial conditions.
Equilibria and Eigenvalues
Calculate supported ODE equilibria, inspect Jacobian eigenvalues, and report local linear stability responsibly.
Sprott Explorer
Understand codes, decoding, search, filtering, visual presets, and local user-owned dictionaries.
Models and research practice
5 guidesCreate a Custom System
Define, validate, simulate, import, and export a flow or map with the no-code editor.
Concept Dictionary
Use the built-in dictionary as a learning aid and connect definitions to plots and numerical experiments.
Export and Reproducibility
Save figures and definitions, record the numerical contract, and build a result package another person can audit.
Research Workflows
Plan parameter studies, comparison matrices, multistability screens, and evidence-preserving exploratory campaigns.
Scientific Interpretation
Separate what plots and finite computations show from claims that require convergence studies or formal analysis.