Plot combined 2D and 3D phase portraits for chaotic systems

Simple code for plotting visually pleasing 2D and 3D phase portraits for dynamical systems in a single figure

The following code can be used to plot the solution of a dynamical system, either with respect to time, or with respect to the relation between the states. The second diagrams are commonly termed phase diagrams or phase portraits, and give the attractor of the system. Some comments are added to make the graph print ready, for papers etc. The Lorenz system is used as an example.

The 3d phase portraits are combined with the 2D projections in a single graph, giving a nice visual representation of the attractor shape.

Illustrative video:

https://www.youtube.com/watch?v=CRE_3-uoCyw

Indicative research papers

https://www.stevenstrogatz.com/books/nonlinear-dynamics-and-chaos-with-applications-to-physics-biology-chemistry-and-engineering

https://ieeexplore.ieee.org/abstract/document/9703188

https://www.mdpi.com/2227-7080/7/4/76

https://www.mdpi.com/2673-8716/2/2/8

https://link.springer.com/article/10.1007/s40435-020-00712-0

Youtube channel: https://www.youtube.com/@lazarosmoysis5095