toolbox_chaos
v0.1.0
Python 3.10+ - PyQt6 GUI - v0.1.0 Stable

Fyskode Chaotic Systems Toolbox

Fyskode Chaotic Systems Toolbox is a PyQt6 desktop application for exploring chaotic dynamical systems through numerical simulation, visualization, and diagnostic analysis.

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About

Project metadata, archive reference, and build baseline.

Version
0.1.0
License
MIT License
Archive
OSF DOI 10.17605/OSF.IO/GQMJR
Platforms
Windows, macOS, Linux
Interface
13 scientific tabs and 38 registered systems
Built With
Python 3.10+, PyQt6, NumPy, Matplotlib
Architecture
Toolbox Chaos GUI + Hidden Attractors FO mathematical engine
Author
Maria Fernanda Moreno Lopez (Fer Moreno) / Xerkkun
Repository
github.com/Xerkkun/Toolbox-chaos

Key Features

Desktop tools for simulation, visual analysis, and reproducible figure generation.

3D
38 Registered Systems
Load flows, maps, delay models, neuronal systems, the Sprott A-S family, Lorenz-96, and a 4D hyperchaotic model from one selector.
2D
3D and 2D Geometry
Generate 3D trajectories, compare the xy, xz, and yz projections, and reuse the same simulation across views.
TS
Reusable Time Series
Inspect state variables versus time and send the last trajectory directly to portraits or spectral analysis without recomputing it.
RK
Integrator Comparison
Overlay Euler, Heun/RK2, and RK4 trajectories to study step-size sensitivity and select an appropriate numerical method.
PS
Welch PSD and Amplitude
Estimate a Welch power spectral density or amplitude spectrum with physical frequency units and a configurable transient.
EV
Equilibria and Eigenvalues
Locate equilibria of ODE flows, inspect eigenvalues in the complex plane, and read their local stability classification.
fx
No-code Custom Systems
Define a flow or map with safe expressions, validate it, simulate it, and exchange complete definitions as JSON.
SP
Sprott Explorer
Decode and generate compact systems, run examples, search candidates, manage a local gallery, and export figures, trajectories, and metadata.
CO
Coexisting Attractors
Compare multiple trajectories produced by one parameter set and different initial conditions in included reference cases.
BA
Basins of Attraction
Classify a plane of initial conditions by long-term destination and inspect representative trajectories and equilibrium markers.
BF
Bifurcation Diagrams
Sweep one parameter, discard the transient, retain an observable, and compare branches or attractor responses.
LY
Lyapunov Diagnostics
Estimate finite-time Lyapunov spectra for 3D ODE flows and inspect convergence before interpreting the result.
PDF
Local Scientific Dictionary
Open the bundled dictionary and supporting documents directly from the application while interpreting each diagnostic.
EX
Research-ready Export
Save scientific figures and, in Sprott workflows, export trajectory CSV, metadata JSON, local galleries, and Markdown explanations.

Concept-first toolbox

Learning Chaos With Figures

Toolbox Chaos is organized around the same teaching idea as the dictionary PDF: students learn faster when each concept is tied to a concrete graph. The overview shows the available workflows; the documentation explains how to read each graph in detail.

Read the visual theory primer ->

Theory Through Graphics

The dictionary and web documentation connect definitions with reproducible figures, so students can read what each diagnostic is actually showing.

Separate Visual Tasks

A basin map, a coexistence comparison, a bifurcation diagram, and a Lyapunov plot answer different questions. The site keeps those workflows separated.

Reproducible Examples

Examples use explicit systems, parameters, initial conditions, projection choices, and retained windows so students can reproduce the plots.

Compact-system exploration workflow

Sprott Explorer

The Sprott Explorer invites students to experiment with compact dynamical-system recipes inspired by J. C. Sprott's strange-attractor work. Load a generated example, change the projection or visual preset, and watch how a short code becomes a map, a flow, or a dense phase-space object worth investigating.

The public page uses reproducible educational examples, while the documentation explains the decoding logic, search filters, plotting choices, and parameter effects.

Open the Sprott guide ->
Generated Sprott-style flow with depth coloring
Depth-colored flow
Generated Sprott-style 3D map with color-coded coordinate
3D map projection
Generated Sprott-style 4D projection with hidden coordinate color
4D color projection

Working Pattern

A practical loop for moving from a first run to a figure worth saving.

1

Choose a scientific question

Start from the view or comparison you need: trajectory geometry, time evolution, integration method, spectrum, bifurcation, basin, coexistence, or local stability.

2

Load a coherent preset

Use a registered system so equations, parameters, initial state, and integration scale begin in a known range.

3

Run a low-cost pass

Use coarse grids, shorter sweeps, or fewer points to check whether the selected region is meaningful.

4

Refine one control

Change one value at a time: time step, total time, transient, parameter range, projection, or density.

5

Compare complementary evidence

Use geometry, time series, method comparison, spectra, eigenvalues, basins, bifurcation, and Lyapunov estimates for distinct questions.

6

Record and export

Save the system, parameters, initial conditions, method, step, transient, and figure or data artifact needed to reproduce the run.

Practical Guides

The complete guide set covers installation, every major GUI workflow, figures, exports, research applications, and responsible interpretation.

View all guides ->
Beginner Read ->

Getting Started

Install the desktop application, run a first catalog example, reuse its trajectory, and save a figure.

Beginner Read ->

Interface Overview

Understand the 13 tabs, shared trajectory workflow, controls, status messages, and where each task belongs.

Beginner Read ->

System Catalog

Choose among 38 registered flows, maps, delay and special models without confusing catalog status with a dynamical claim.

Beginner Read ->

Concepts and Visual Theory of Chaos

Definitions, figures, and reading strategies for students entering chaotic systems for the first time.

Beginner Read ->

Lorenz Attractor Quick Start

Set parameters, run a first simulation, and compare 3D phase space with projected 2D portraits.

Beginner Read ->

3D Attractor View

Configure a three-dimensional catalog simulation, inspect projections, and distinguish geometry from proof of attraction.

Beginner Read ->

2D Phase Portraits

Select state-variable pairs, reuse a trajectory, and read folds, loops, crossings, and projection artifacts.

Beginner Read ->

Time Series

Inspect state histories, transients, oscillations, bursts, drift, and numerical failure before deeper analysis.

Intermediate Read ->

Compare Integration Methods

Compare Euler, Heun, and RK4 under the same numerical contract and perform a practical step-size study.

Intermediate Read ->

Spectral Analysis

Choose Welch PSD or an amplitude spectrum, discard transients, set frequency limits, and interpret units correctly.

Intermediate Read ->

FFT Example

A focused example for generating and reading the Lorenz amplitude spectrum.

Intermediate Read ->

Lyapunov Exponent Diagnostics

Visualize perturbation growth and read convergence-aware finite-time exponent estimates.

Intermediate Read ->

Bifurcation Diagrams

Configure parameter sweeps, retained points, Poincare sections, and Hopf examples.

Intermediate Read ->

Basins of Attraction

Read finite-resolution basin maps and representative trajectories launched from different regions.

Intermediate Read ->

Coexisting Attractors

Compare registered multistability cases under fixed parameters and distinct initial conditions.

Intermediate Read ->

Equilibria and Eigenvalues

Calculate supported ODE equilibria, inspect Jacobian eigenvalues, and report local linear stability responsibly.

Intermediate Read ->

Sprott Explorer

Understand codes, decoding, search, filtering, visual presets, and local user-owned dictionaries.

Intermediate Read ->

Create a Custom System

Define, validate, simulate, import, and export a flow or map with the no-code editor.

Beginner Read ->

Concept Dictionary

Use the built-in dictionary as a learning aid and connect definitions to plots and numerical experiments.

Intermediate Read ->

Export and Reproducibility

Save figures and definitions, record the numerical contract, and build a result package another person can audit.

Advanced Read ->

Research Workflows

Plan parameter studies, comparison matrices, multistability screens, and evidence-preserving exploratory campaigns.

Advanced Read ->

Scientific Interpretation

Separate what plots and finite computations show from claims that require convergence studies or formal analysis.

Visual Output Gallery

Current GUI workspaces plus representative attractors, bifurcations, Poincare sections, basins, coexistence cases, Lyapunov figures, and Sprott-generated graphics.

Toolbox Chaos 3D attractor tab showing a Lorenz trajectory
Current interface

3D attractor workspace

Select a registered model, edit parameters and initial conditions, then generate a 3D trajectory.

Toolbox Chaos 2D phase portraits tab
Current interface

Phase-portrait workspace

Reuse the last trajectory and compare the xy, xz, and yz projections in one view.

Toolbox Chaos time-series tab
Current interface

Time-series workspace

Inspect each state variable against time while retaining the numerical context of the simulation.

Toolbox Chaos spectral tab showing a Welch power spectral density
Current interface

Welch power spectral density

Choose Welch PSD or an amplitude spectrum, set the transient and frequency range, and preserve physical units.

Toolbox Chaos numerical integrator comparison tab
Current interface

Euler, Heun, and RK4

Overlay three supported integrators to reveal method and time-step sensitivity.

Toolbox Chaos equilibria and eigenvalues tab
Current interface

Equilibria and eigenvalues

List equilibria, plot eigenvalues on the complex plane, and inspect local stability labels.

Toolbox Chaos Lyapunov tab showing the finite-time Lorenz spectrum
Current interface

Lyapunov convergence

Estimate the finite-time Lyapunov spectrum and inspect every convergence curve with its numerical contract.

Toolbox Chaos bifurcation tab showing a Lorenz rho sweep
Current interface

Bifurcation sweep

Sweep a declared parameter and retain Poincare events after a documented transient.

Toolbox Chaos basin tab showing a Lorenz initial-condition classification
Current interface

Basin classification

Classify a grid of initial conditions and overlay the supported equilibria on the sampled plane.

Toolbox Chaos coexistence tab showing the registered Lorenz case
Current interface

Coexistence workspace

Load a referenced case and compare trajectories generated from multiple registered initial conditions.

Toolbox Chaos dictionary tab displaying the bundled PDF reference
Current interface

Embedded concept dictionary

Read the bundled mathematical and technical reference without leaving the application.

Toolbox Chaos custom-system editor
Current interface

No-code system editor

Define equations and parameters, validate safe expressions, simulate, and exchange the model as JSON.

Toolbox Chaos Sprott Explorer home tab
Current interface

Sprott Explorer

Move from tutorial and compact code to examples, exploration, local inventory, gallery, and explained backend.

Animated 3D Lorenz attractor rendered in the Toolbox Chaos visual style
3D attractors

Lorenz 3D rotation

Animated orbit rendered with the toolbox magenta trajectory style.

Chua double-scroll attractor with time-series panels
3D attractors

Chua double scroll

Double-scroll flow with the same phase-and-series layout used by the toolbox.

Lorenz 3D trajectory with 2D phase portraits projected onto coordinate planes
Phase portraits

Projected Lorenz portraits

2D phase portraits overlaid on the planes of a 3D Lorenz figure.

Separate Lorenz 2D phase portraits
Phase portraits

2D projection grid

x-y, x-z, and y-z portraits shown separately for comparison.

Logistic bifurcation diagram generated by Fyskode Chaos Toolbox
Bifurcation

Logistic cascade

Classic period-doubling cascade and dense chaotic bands.

Lorenz bifurcation sweep over rho
Bifurcation

Lorenz rho sweep

Higher-density local maxima of z as rho changes in the Lorenz system.

Lorenz Poincare section showing crossings on a plane
Poincare

Lorenz return section

A 3D flow reduced to crossing points on a selected plane.

Supercritical Hopf bifurcation example with phase portraits
Bifurcation

Hopf example

A stable equilibrium changes into a stable limit cycle.

Lorenz basin map generated by Fyskode Chaos Toolbox
Basins

Lorenz basin map

Grid of initial conditions classified by long-term destination.

Lorenz basin map with representative trajectories
Basins

Basin trajectories

Representative orbits launched from different colored basin regions.

Lorenz coexisting stable states generated from two initial conditions
Coexistence

Lorenz coexistence

Same Lorenz parameters, two initial conditions, two stable destinations.

Animated Lorenz coexisting trajectories
Coexistence

Simultaneous starts

Animation showing both Lorenz coexistence trajectories generated together.

Perturbation expansion and contraction concept diagram
Lyapunov

Perturbation geometry

Expansion and contraction directions behind Lyapunov exponents.

Synthetic Sprott-style flow with depth coloring
Sprott Explorer

Depth-colored flow

A generated Sprott-style flow rendered with depth coloring.

Synthetic 3D Sprott map with coordinate coloring
Sprott Explorer

3D color map

Projection uses color to keep a hidden coordinate readable.

Synthetic 4D Sprott map projected with color
Sprott Explorer

4D projection

A 4D synthetic map projected with the fourth coordinate in color.

Citing Fyskode Chaos Toolbox

If you use this software in research, thesis, or academic workflows, cite the archived OSF release.

Maria Fernanda Moreno Lopez. Fyskode Chaotic Systems Toolbox, version 0.1.0. 10.17605/OSF.IO/GQMJR.

Get BibTeX and CFF files ->