Separatrix user guide
Separatrix draws phase portraits, cobwebs, Poincaré sections, Lyapunov spectra, orbit diagrams, bifurcation branches and curves of bifurcations in two parameters of the systems you type. This guide has one page per task or view. To install the app first, follow the guide for Windows, macOS or Linux.
Start here
- Getting started. Open an example, add a trajectory, drag a parameter, save and export.
- Enter equations. Flows, maps, higher-order and Hamiltonian systems, in LaTeX or plain text.
The views
The View control in the right-hand panel switches between views. A flow offers Phase, Series, Section, 3D, λ, Branch and Parameter plane. A map offers Phase, Series, Cobweb, λ, Orbit, Branch and Parameter plane. A view that doesn't fit the system is grayed out, and the panel says why.
| View | Control | Page | Example project |
|---|---|---|---|
| Phase plane | Phase | Phase plane | phase-plane.sepx |
| Time series | Series | Time series | time-series.sepx |
| Cobweb | Cobweb | Cobweb | cobweb.sepx |
| 3D view | 3D | 3D view | 3d-view.sepx |
| Poincaré section | Section | Poincaré section | poincare-section.sepx |
| Lyapunov spectrum | λ | Lyapunov spectrum | lyapunov.sepx |
| Orbit diagram | Orbit | Orbit diagram | orbit-diagram.sepx |
| Continuation | Branch | Continuation | continuation.sepx |
| Parameter plane | Parameter plane | Parameter plane | parameter-plane.sepx |
Each example project opens in its view. Download it and open it with Open…, or drop it on the Separatrix window.
Share and present
- Export figures and data. LaTeX, SVG, PNG and CSV.
- Project files. Save, open, recent files and drag-and-drop.
- Projector mode. A light theme with larger type for the lecture hall.
- Keyboard shortcuts. Every key the app answers to.
Where the numbers come from
Separatrix checks its numbers against published values on every change. Four scripts in the
repository print one row per claim: scripts/strogatz-gate.sh for the chapter 2 to 8 examples of
Strogatz's Nonlinear Dynamics and Chaos (2nd edition), scripts/chaos-gate.sh for Lyapunov
exponents and period doublings, scripts/continuation-gate.sh for bifurcation points, and
scripts/codim2-gate.sh for the points where curves in two parameters meet. The
numbers quoted in this guide are copied from their output. CONTRIBUTING.md
says how to run them.
The screenshots come from the real app. bash scripts/docs-screenshots.sh opens each example
project and saves docs/media/<view>.png.