Lyapunov Exponent Diagram for 1D Chaotic Maps

Version 1.0.0 (2.39 KB) by Lazaros Moysis
Plot the Lyapunov Exponent Diagram for any Chaotic Map
0.0
(0)
105 Downloads
Updated 3 Mar 2024

View License

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

Cite As

Lazaros Moysis (2024). Lyapunov Exponent Diagram for 1D Chaotic Maps (https://www.mathworks.com/matlabcentral/fileexchange/160556-lyapunov-exponent-diagram-for-1d-chaotic-maps), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2023b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired by: Density-Colored Bifurcation Diagrams

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Version Published Release Notes
1.0.0