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Software version, DOI, platforms, and architecture.
Simulation and Analysis Functions
Desktop tools for simulation, visual analysis, and reproducible figure generation.
Definitions linked to numerical results
Reading Trajectories and Diagnostics
The PDF dictionary and web guides connect dynamical-systems concepts with figures produced under explicit numerical contracts. This page identifies the available calculations, while each guide develops the configuration, result interpretation, and supporting data.
Study the dynamical-systems concepts -> Follow the complete university pathway in Learning →Definitions and Reproducible Figures
The dictionary and web guides connect each definition with a reproducible figure and explain the quantity calculated by each diagnostic.
Basins, Bifurcations, and Lyapunov Rates
A basin map classifies initial conditions; the coexistence view contrasts destinations; a bifurcation diagram scans a parameter; and a Lyapunov plot estimates separation rates.
Parameters and Initial Conditions
Each example records the system, parameters, initial condition, projection, and retained window so another run can reconstruct the plot.
Compact-system exploration workflow
Sprott Explorer
The Sprott Explorer decodes compact descriptions inspired by J. C. Sprott's work on strange attractors. Starting from a generated example, it lets the user adjust the projection and graphical parameters to compute maps, flows, and dense phase-space representations.
The public examples record their computational settings. The guide develops the decoding logic, search filters, plotting choices, and the effect of each parameter.
Open the Sprott guide ->
Numerical Experiment Sequence
The question determines the model, integration contract, refinement study, and files that document the run.
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.
Load a coherent preset
Use a registered system so equations, parameters, initial state, and integration scale begin in a known range.
Compute a low-resolution reference
Use a preliminary grid, a short sweep, or a small point set to verify the interval and estimate the computational cost.
Refine one control
Change one value at a time: time step, total time, transient, parameter range, projection, or density.
Relate trajectories, spectra, and stability
Connect geometry and time series with integration methods, spectra, eigenvalues, basins, bifurcations, or Lyapunov estimates according to the research question.
Record and export
Save the system, parameters, initial conditions, method, step, transient, and figure or data artifact needed to reproduce the run.
Interface Procedures
The guides cover installation, panel configuration, figure generation, export, and the scientific criteria used to interpret each calculation.
Installation 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.
Lorenz 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.
Spectral 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.
Create 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.
Visual Output Gallery
Current GUI workspaces plus representative attractors, bifurcations, Poincare sections, basins, coexistence cases, Lyapunov figures, and Sprott-generated graphics.
Citing Toolbox Chaos
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.