Lyapunov Exponent Diagram for 1D Chaotic Maps

Plot the Lyapunov Exponent Diagram for any Chaotic Map

The code computes the Lyapunov exponent for a 1d chaotic map. The logistic map is used as an example, but you can replace this with any given map.

The methodology is implemented from the following work:

Bovy, J. (2004). Lyapunov exponents and strange attractors in discrete and continuous dynamical systems. Theoretica Phys. Project, Catholic Univ. Leuven, Flanders, Belgium, Tech. Rep, 9, 1-19.

Relevant references:

https://www.mdpi.com/2073-8994/15/12/2138

https://www.mdpi.com/2073-8994/15/3/726

https://www.mdpi.com/2227-7390/10/15/2801

https://dergipark.org.tr/en/pub/chaos/issue/54264/756229

The code below is broken into 2 parts. The first section is used to plot the LE diagram.

The second part is used to plot the bifurcation diagram, and overlap the LE diagram above it. This combination can be done to illustrate that the LE is negative on non-chaotic regions, and positive on chaotic regions.

Lazaros Moysis

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

RG: https://www.researchgate.net/profile/Lazaros-Moysis