toolbox_chaos v0.1.0
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Toolbox Chaos procedure

Reproducible Research Workflows

Turn GUI exploration into bounded, traceable studies of parameters, initial conditions, numerical sensitivity, spectra, stability, and multistability.

Level Advanced
GUI tab Multiple tabs, selected by the research question
Research question How can a research team use Toolbox Chaos systematically to build evidence from controlled numerical experiments?

Question and result

Calculation performed

Design an exploratory campaign in which every claim has a matching GUI operation, saved output, and verification step.

Required configuration

  • Write a specific question, independent variables, fixed controls, output metrics, and stopping criterion before running a large grid.
  • Establish a baseline simulation and a reproducible export convention.
  • Distinguish exploratory evidence from formal proof and from specialized analyses performed outside Toolbox Chaos.

Panel and figure

Displayed quantities

Finite-resolution bifurcation diagram over a declared parameter interval
A parameter sweep replaces isolated handpicked portraits with a declared sampling design.
Finite-time trajectory-separation diagnostic
A diagnostic is strongest when paired with resolution, horizon, and trajectory checks.
Finite-resolution basin visualization for a bistable system
Initial-condition maps are conditional on the plane, domain, resolution, horizon, and destination classifier.

Configuration and calculation

Control sequence

  1. Frame one testable question

    Examples include how a portrait changes with one parameter, whether a spectral peak persists under refinement, or whether registered initial conditions reach visibly distinct long-time states.

    Avoid broad goals such as ‘find chaos.’ Define the computed output and what outcome would be considered continue, reformulate, or discard.

  2. Establish the baseline

    Use Atractor 3D, Retratos 2D, and Series temporales to check boundedness, transient duration, state scale, and useful observables.

    Use Comparar metodos and step refinement before committing to a costly sweep.

  3. Choose the exploration axis

    For one model parameter, use Bifurcación with a declared range and sampling density. For initial states, use Coexistencia or Cuenca de atracción only where their registered cases or classifiers are supported.

    For a small hypothesis-driven comparison, use a run matrix with one changed factor and saved portraits, time series, or spectra.

  4. Add the matching diagnostic

    Use Espectro for frequency structure, Lyapunov for the supported finite-time 3D ODE-flow calculation, and Autovalores for supported local equilibrium analysis.

    Use each diagnostic within the model type, dimension, and numerical contract stated by its tab.

  5. Repeat and refine

    Repeat selected cases with a smaller step, longer horizon, different transient, and nearby initial states. Increase sweep or basin resolution only after the coarse campaign identifies a bounded region worth refining.

    Preserve divergent, inconclusive, and contradictory cases; they determine the limits of the study.

  6. Report an evidence matrix

    For each conclusion, list the direct output, numerical checks, alternative explanations, and remaining limitations.

    Use language such as ‘finite-time estimate,’ ‘at the tested grid resolution,’ and ‘for the sampled initial conditions’ whenever those qualifiers define the evidence.

Four reusable study patterns

  • Parameter study: baseline → bifurcation sweep → selected portraits/time series → diagnostic → step and grid refinement.
  • Initial-condition study: fixed parameters → declared plane/domain → basin or registered coexistence comparison → representative trajectories → resolution and horizon checks.
  • Numerical study: fixed model → Euler/Heun/RK4 comparison → step ladder → stable summary quantities → method choice with limitations.
  • Custom-model pilot: validate JSON definition → baseline simulation → independent equation check → numerical refinement → decide whether specialized code is needed.

Record

Computed data

  • A baseline plus a structured parameter or initial-condition campaign with declared controls.
  • A set of figures and settings records linked to specific research questions.
  • An evidence matrix that distinguishes supported conclusions, provisional inferences, and unresolved cases.

Scientific reading

Interpretation criteria

A robust exploratory finding persists across relevant resolution and horizon changes and appears across complementary views or diagnostics.

Contradictory diagnostics identify a transient, numerical, model-compatibility, or interpretation question for the next refinement step.

Files

Experiment record

  • Predeclared question, varied factor, fixed controls, grid, and stopping rule.
  • Baseline and refinement runs with complete numerical contracts.
  • All direct outputs, including failures and null or unresolved cases.
  • A claim-to-evidence table and a separate list of analyses performed outside the GUI.

Applications

Questions addressed by the calculation

  • Parameter-regime mapping and hypothesis generation.
  • Numerical-method sensitivity studies.
  • Teaching laboratories on bifurcation, spectra, stability, and multistability.
  • Preparation of bounded pilot studies before custom code or high-performance campaigns.

Scope

Evidence conditions

  • Toolbox Chaos is an exploratory GUI; large campaigns may require scripted workflows, external statistics, or specialized solvers.
  • Finite parameter and initial-condition grids report the sampled domain, resolution, and observed classes; global completeness requires a broader mathematical analysis.
  • Hidden-attractor localization and certification belong to the separate Hidden Attractors FO research workflow.