Bifurcation diagram for the Lorenz Chaotic system

Compute the bifurcation, or continuation, diagram for the Lorenz chaotic system

This code can be used to compute the bifurcation diagram for the Lorenz chaotic system.

The diagram is generated by simulating the system from fixed initial conditions, and after discarding the transient, computing the intersections of the trajectory with a given plane of choice, and a specific direction.

The code can be easily adapted to compute a continuation diagram, where after each simulation, the initial condition is set equal to the final value of the previous simulation.

The code can also be easily adapted to any chaotic system, not just the Lorenz. What you need to do is replace the lorenz call in the ode45 with any chaotic system of your choice. Of course, you must first study the system to choose the appropriate plane of intersection for the system's trajectory.

An illustrative video explaining the bifurcation diagram can be found below.

https://www.youtube.com/watch?v=OXTS-d9HdB4

A video explaining the code is available here:

https://www.youtube.com/watch?v=O506G8DtmQk

An illustrative video for the continuation diagram can be found below.

https://www.youtube.com/watch?v=vXOK45HbvBU

References:

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

https://www.hindawi.com/journals/complexity/2020/2826850/

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