Explaining the Bifurcation Diagram for the Lorenz Chaotic System

Описание: An instructional video on what the bifurcation diagram represents, and how to plot it. The Lorenz chaotic system is used as an example, being one of the most well known chaotic systems.

Matlab code: https://uk.mathworks.com/matlabcentra...

Video explaining the code:    • How to plot the Bifurcation Diagram of the...  

Full playlist:    • Chaotic Systems Theory and MATLAB  

Papers on bifurcation diagrams:
-- https://ieeexplore.ieee.org/abstract/...
-- https://www.hindawi.com/journals/comp...
-- https://www.mdpi.com/2227-7080/7/4/76
-- https://www.mdpi.com/2673-4001/1/3/19
-- https://www.mdpi.com/2673-8716/2/2/8
-- https://link.springer.com/article/10....

Chaos theory studies how small changes in initial conditions can lead to vastly different outcomes in certain systems, making long-term prediction nearly impossible. It’s often illustrated by the “butterfly effect,” where something as tiny as a butterfly flapping its wings could, in theory, influence weather patterns weeks later. Despite appearing random, chaotic systems follow underlying deterministic rules—they’re just incredibly sensitive, so their complexity hides their order.

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