Bifurcation diagram for the Lorenz system (local maxima)

Compute the bifurcation, or continuation, diagram for the Lorenz chaotic system through the local maxima method

This code can be used to compute the bifurcation diagram for the Lorenz chaotic system using the local maxima method.

This is alternative method to plotting the points of intersection with a given plane. Here, we only compute the local maxima of a chosen state, and plot them.

The diagram is generated by simulating the system from fixed initial conditions, and after discarding the transient, finding the local peaks of a given state.

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.

For information on the method, check:

Moysis, L., Lawnik, M., Fragulis, G. F., & Volos, C. (2025). Continuous-Time Density-Colored Bifurcation Diagrams. International Journal of Bifurcation and Chaos, 2530028.

https://www.worldscientific.com/doi/10.1142/S0218127425300289

https://www.researchgate.net/publication/394842432_Continuous-Time_Density-Colored_Bifurcation_Diagrams

Please cite this work if you use the code.

https://www.youtube.com/watch?v=jkrmZB9OM2E

https://www.youtube.com/watch?v=p9mg6TOBMY0

https://www.youtube.com/watch?v=8kKkq2mk7gA

Channel: https://www.youtube.com/@lazaros_moysis