Toolbox Chaos documentation
Simulation, diagnostics, and result records
Use the desktop GUI to define numerical experiments, simulate registered or custom dynamical systems, connect visual and diagnostic views, explore parameters and initial conditions, and export traceable results. Each guide identifies the relevant tab, procedure, expected output, interpretation, applications, result record, and evidence conditions.
Installation and catalog
4 guidesInstallation and First Simulation
Install the desktop application, run a first catalog example, reuse its trajectory, and save a figure.
Interface Panels and Shared Trajectory
Understand the 13 tabs, shared trajectory workflow, controls, status messages, and where each task belongs.
System Catalog
Choose among 38 registered flows, maps, delay models, and special models; the catalog entry identifies implementation status and the numerical run supplies the dynamical evidence.
Flows, Stability, and Chaotic Dynamics
Definitions and figures for phase space, stability, bifurcations, sensitivity, and chaotic dynamics.
Simulation and visualization
5 guidesLorenz 3D Trajectory and 2D Projections
Set parameters, run a first simulation, and compare 3D phase space with projected 2D portraits.
3D Trajectories and Coordinate Projections
Configure a three-dimensional catalog simulation, inspect its projections, and record the finite trajectory represented by the plot.
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, files, and evidence
5 guidesCreate a Custom System
Define, validate, simulate, import, and export a flow or map with the expression editor.
Concept Dictionary
Use the built-in dictionary as a learning aid and connect definitions to plots and numerical experiments.
Figures, Definitions, and Run Records
Save figures and definitions, record the numerical contract, and build a result package another person can audit.
Parameter Studies and Multistability Screens
Plan parameter studies, comparison matrices, multistability screens, and evidence-preserving exploratory campaigns.
Evidence from Finite Numerical Diagnostics
State the quantities shown by plots and finite computations, then attach the convergence studies or formal analysis required by the claim.