SKHiPPR [ˈski-pr] is a Python toolbox with focus on Stability using the Koopman-Hill Projection method for Periodic solutions and Resonance curves.
SKHiPPR is a continuation toolbox developed by Fabia Bayer as part of a research project in close cooperation with Remco Leine at the Institute for Nonlinear Mechanics, University of Stuttgart, Germany. In this project, we investigate the properties of a Koopman-based Hill stability method for periodic solutions.
For more information about the Koopman-Hill projection method, please see the following references:
- Bayer and Leine (2023): Sorting-free Hill-based stability analysis of periodic solutions through Koopman analysis. Nonlinear Dyn 111, 8439–8466, https://doi.org/10.1007/s11071-023-08247-7.
- Bayer et al. (2024): Koopman-Hill Stability Computation of Periodic Orbits in Polynomial Dynamical Systems Using a Real-Valued Quadratic Harmonic Balance Formulation. International Journal of Non-Linear Mechanics, 167, 104894, https://doi.org/10.1016/j.ijnonlinmec.2024.104894.
- Bayer and Leine (2025, preprint): Explicit error bounds and guaranteed convergence of the Koopman-Hill projection stability method for linear time-periodic dynamics, https://arxiv.org/abs/2503.21318
- Project website: https://www.inm.uni-stuttgart.de/research_nonlinear_mechanics/project_bayer/
The SKHiPPR toolbox is object-oriented and modularized. It generates continuation curves with stability information using an ODE object, Harmonic Balance residual equation, a stability method, and a continuation wrapper.
For technical details about installation and usage, please refer to the documentation.