toolbox_chaos v0.1.0
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Toolbox Chaos procedure

Registered Dynamical Systems

Navigate 38 registered examples, recognize model families and supported dimensions, and choose a system that matches the question you want to investigate.

Level Beginner
GUI tab System selector in the numerical tabs
Research question Which models are available, and how should I choose among flows, maps, delay models, and special displays?

Question and result

Calculation performed

Select an appropriate registered system from its catalog label and parameter contract; state scientific conclusions through the supporting numerical evidence.

Required configuration

  • Know whether your question concerns continuous time, discrete iteration, delay dynamics, or comparison across model families.
  • Consult the cited source for a model before using its equations or parameters in a publication.

Panel and figure

Displayed quantities

Lorenz system phase trajectory
Lorenz is a useful flow baseline because its two-lobed phase-space geometry is widely recognizable.
Side-by-side phase-space comparison of Lorenz, Rossler, and Sprott flows
The middle panel shows how Rössler contrasts with Lorenz and Sprott under a different vector field and parameter set.
Vector field, nullclines, and representative planar trajectories
This field atlas emphasizes the rule that also governs Chua: every visual interpretation must remain tied to the model’s own equations and parameter conventions.

Configuration and calculation

Control sequence

  1. Choose the model family

    Use an ODE flow when step size and physical or nondimensional time are central. Use a map when the state advances by iterations. Mackey–Glass uses a delay-model workflow with a history, while ordinary ODE models use an initial-state workflow.

    Lorenz-96 and the four-dimensional hyperchaotic Lorenz example have display-specific considerations; inspect the interface response after selection.

  2. Read the populated metadata

    After selecting a system, read the parameter labels in their displayed order, the initial-state labels, default values, and dimension-dependent controls.

    Use the parameter vector displayed by the selected model, with its names, order, and units.

  3. Run the registered baseline

    Generate a portrait and time series using the preset before changing a parameter. Save this baseline as the reference for later comparisons.

    Check boundedness and transient behavior. A preset provides an entry point for exploration; reproduction requires the declared horizon, step, and diagnostics.

  4. Vary one declared input

    Change one parameter or one initial-state component while keeping the method, step, and horizon fixed. Use a structured series with the range, increment, and retained diagnostics recorded.

    For a broad interval, use Bifurcación or a documented research workflow with the sampled values retained.

  5. Check feature compatibility

    The 3D view requires a three-state display, analytical or numerical equilibria are restricted to supported ODE flows, and Lyapunov uses its stated 3D ODE-flow contract.

    Basin and coexistence panels depend on registered cases or destination rules; each tab reports the model support available for its diagnostic.

Registered model groups

The current selector contains 38 implemented entries. The grouping below is for navigation; the GUI remains the authority for the exact parameter order and defaults.

  • Continuous three-state examples: Lorenz, Rössler, Chua / double scroll, Chen, Wang–Chen with variable equilibria, Nazarimehr with a line of equilibria, Lü, Duffing–Ueda, Rabinovich–Fabrikant, Rikitake, Unified Lorenz–Chen, Thomas / labyrinth, and Hindmarsh–Rose.
  • Discrete maps: Hénon, logistic, and Ikeda.
  • Delay and special displays: Mackey–Glass, Lorenz-96, and the four-dimensional hyperchaotic Lorenz model.
  • Classic compact flows: Sprott A through Sprott S, nineteen separate catalog entries.

Choosing by research question

  • Sensitivity and phase-space teaching: begin with Lorenz or Rössler.
  • Discrete iteration and period-doubling: begin with the logistic or Hénon map.
  • Circuit-inspired piecewise dynamics: use Chua and preserve its parameter convention.
  • Slow–fast or bursting behavior: inspect Hindmarsh–Rose through time series before geometric projections.
  • High-dimensional or delay behavior: state explicitly which variables or embedding are displayed; the full state-space record includes every modeled coordinate.

Record

Computed data

  • A baseline run whose system type, parameter order, state dimension, initial condition, and numerical settings are all recorded.
  • A defensible reason for selecting the model and the tabs used to study it.

Scientific reading

Interpretation criteria

The catalog organizes implemented examples and supplies operational defaults. Classification of a generated orbit uses the diagnostics and evidence appropriate to the stated claim.

Comparisons across systems are meaningful only when the numerical resolution, discarded transient, observed duration, and plotted variables are made explicit.

Files

Experiment record

  • Use the full catalog label and cite the scientific source for the equations.
  • Record flow, map, delay, or special-display status and the variables actually plotted.
  • Keep the untouched preset result alongside parameter-modified results.

Applications

Questions addressed by the calculation

  • Comparative teaching examples for continuous and discrete dynamics.
  • Benchmarking numerical methods across different nonlinear vector fields.
  • Selecting candidate models for parameter, spectral, stability, or multistability studies.

Scope

Evidence conditions

  • A catalog entry supplies an implemented model and a starting regime for a documented parameter study.
  • Sprott A–S catalog flows are distinct from the separate Explorador Sprott code and local-dictionary workflow.
  • Published hidden-dynamics claims retain their original evidence; Toolbox Chaos results record the GUI workflow used for simulation and visualization.