toolbox_chaos v0.1.0
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Toolbox Chaos practical guide

Time Series

Read each state variable against time or iteration, identify transients and numerical warning signs, and prepare signals for spectral or comparative analysis.

Level Beginner
GUI tab Series temporales
Research question Does the trajectory settle, oscillate, burst, drift, switch regimes, or become numerically unreliable over time?

Objective

What you will accomplish

Establish what the computed state does over the observation window before interpreting a phase portrait or diagnostic.

Before you begin

  • Choose a model and numerical contract, or retain a compatible shared trajectory from another tab.
  • For maps, interpret the horizontal axis as iteration rather than continuous physical time.

Reference outputs

What these views can show

Current Series temporales tab with Lorenz x, y, and z histories
The current GUI aligns all state histories on a common time axis and exposes their simulation contract beside the plots.
Lorenz phase trajectory and synchronized state time series
Time traces show when the orbit switches lobes and how the state coordinates co-evolve.
Chua trajectory and synchronized state time series
A second model demonstrates why the transient and observation window must be judged for each system.

Procedure

Step-by-step workflow

  1. Generate or reuse the trajectory

    Select the system and either press Generar series temporales or use the last trajectory created for the same model.

    When comparing views, reuse is preferable because it eliminates an unintended difference in integration settings.

  2. Inspect the beginning of the record

    Identify rapid approach, overshoot, or drift that belongs to the initial transient. Do not silently crop it; record the discarded interval in later analysis.

    If the signal immediately grows without bound or becomes invalid, review step size, parameters, and initial state before interpreting any plot.

  3. Compare variables

    Use separate state panels and colors to examine phase shifts, relative amplitude, slow envelopes, bursts, plateaus, or switching events.

    Avoid comparing raw amplitudes across variables with different physical units unless a documented normalization is applied outside the GUI.

  4. Check observation length

    Extend the duration to determine whether an apparent steady regime persists. A short nearly periodic segment can be a transient or a window inside a longer irregular record.

    For slow–fast models such as Hindmarsh–Rose, ensure the horizon covers several slow cycles rather than only fast spikes.

  5. Perform a resolution check

    Repeat with a smaller step for flows. Compare waveform scale, event timing over early intervals, and qualitative regime.

    Late pointwise divergence is expected in sensitive regimes; use convergence of statistics or qualitative features instead of demanding identical long traces.

  6. Export and hand off

    Save the time-series grid. If continuing to Espectro, use the same trajectory and declare the transient removed there.

    Include the horizontal-axis meaning, units if known, sampling step, and total window in captions or experiment notes.

Result

Expected output

  • One aligned signal per displayed state variable over a known time or iteration window.
  • A documented transient interval and a judgment about whether the remaining window is long enough for the intended analysis.

Interpretation

How to read it

Periodic repetition, quasiperiodic modulation, intermittent bursts, and irregular fluctuations can often be distinguished provisionally in time, but each pattern requires corroboration.

An irregular signal may result from deterministic chaos, a transient, insufficient resolution, delay-model history effects, or numerical instability. The time series alone does not choose among them.

Export

Reproducibility checklist

  • Record step or iteration index, duration, and transient handling.
  • Preserve variable names, units, and any color convention.
  • Use the same window when comparing parameters or methods.

Applications

Where this workflow helps

  • Detecting transients before spectral or Lyapunov analysis.
  • Studying oscillations, slow–fast bursting, switching, and map iterations.
  • Communicating temporal behavior that is hidden by a phase-space projection.

Limits

What it does not establish

  • Visual irregularity is not a chaos test.
  • Aliasing and inadequate sampling can alter apparent oscillations and any downstream spectrum.
  • The panel does not infer basins, attraction, or hiddenness from a signal.