auto-AUTO: A Python Layer for Automatically Running the AUTO-07p Continuation Software

Demaeyer, Jonathan;Hamilton, Oisin
(2025) Journal of Open Source Software — Vol. 10, n° 113, p. 8079 (2025)

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  • Demaeyer, Jonathanorcid-logo
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  • Hamilton, Oisinorcid-logoUCLouvain
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Abstract
auto-AUTO (or AUTO2) is a Python package that acts as an intermediate layer between the user and AUTO-07p continuation software (Doedel et al., 2007) (AUTO from here on). auto-AUTO automates the running of AUTO by monitoring the continuation, while also keeping track of bifurcation points. The package can automatically continue along these branching points, and continue branching along further bifurcation points to attempt to construct full bifurcation trees. To achieve this in a reliable way, AUTO computations are managed by auto-AUTO by setting appropriate stopping conditions, such as meeting other branches, looping branches, and specified bifurcations. These stopping conditions supplement the usual AUTO bounds and ensure that branches of detected solutions are unique and well defined. In addition, auto-AUTO provides a comprehensive and documented Python API to investigate properties of the computed continuations and solutions. auto-AUTO can be run in Jupyter notebooks (Kluyver et al., 2016) and the results can be plotted with Matplotlib (Hunter, 2007) using predefined plotting methods (see Figure 1). This facilitates the integration of the results from AUTO with other Python workflows.
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Demaeyer, J., & Hamilton, O. (2025). auto-AUTO: A Python Layer for Automatically Running the AUTO-07p Continuation Software. Journal of Open Source Software, 10(113), 8079. https://doi.org/10.21105/joss.08079 (Original work published 2025)