auto-AUTO or AUTO² is an AUTO automatic search algorithm codebase to enhance the original AUTO-07p Python interface with a top layer which allows users to:

• automate the continuation of as many branches as possible, branching whenever possible to construct full bifurcation trees, and finishing computations based on a predefined logic (meeting other branches, looping branches, etc...)
• plot results with Matplotlib
• perform these computations in Jupyter notebooks

The package can automatically continue along 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. This allows the user to generate the full bifurcation diagrams in high-dimensional complex dynamical systems, where the number of branches to track may be too large for a human. This tool was used for example to detect relevant periodic orbits in a low order land–atmosphere model (Hamilton et al. 2025, see reference below).

Reference

• 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.
• Hamilton, O., Demaeyer, J., Crucifix, M., & Vannitsem, S. (2025). Using unstable periodic orbits to understand blocking behavior in a low order land–atmosphere model. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(8).