Welcome to PyGhostID’s documentation!

Background

PyGhostID is a Python package for identifying generalized saddle-node ghosts in the vicinity of saddle-node bifurcations and their composite ghost structures such as ghost channels and ghost cycles in dynamical systems. PyGhostID’s main function is the implementation of GhostID, a trajectory-based algorithm to identify saddle-node ghosts in dynamical systems. Besides the main algorithm, additional functions allow users to identify composite structures of ghosts (ghost cycles, channels and networks) and track ghosts versus changing parameters.

Figure 1: (a) flow-diagram of ghostID, (b) data associated with ghost states, (c) functionalities of the PyGhostID package.

Installation

Install the latest version of PyGhostID via pip:

pip install PyGhostID

Contact

For questions or additional information, please write to daniel.koch@umanitoba.ca.

Related Publication

The theory behind PyGhostID and some applications can be found in our research article:

Daniel Koch, Akhilesh Nandan (2026). Generalized saddle-node ghosts and their composite structures in dynamical systems. arxiv: 2604.05194.

All results from the paper can be reproduced using the code available on github.

If you use PyGhostID or its repository in your research, please cite our paper!

Overview

Contents:

• Quickstart
• Tutorials
  • Tutorial 1 - ghostID parameter optimization and trouble-shooting
  • Tutorial 2 - Identifying ghost structures: channels, cycles, networks
  • Tutorial 3 - Tracking ghosts across parameter changes
• Changelog
  • Version 1.0.3
• API Reference
  • PyGhostID package