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Yes it's a really fascinating subject! I'm doing my PhD in oceanography and work with climate simulations. Of course the climate system is quite chaotic, so the whole subject piqued my interest.
I'm fortunate that I'm taking a class in 'chaotic dynamics' currently on campus. We actually just spent a few weeks with the logistic map equation, cobweb diagrams, etc. so this was good timing.
Here's a good MOOC with videos that you'll learn a lot from: https://www.complexityexplorer.org/courses/79-nonlinear-dynamics-mathematical-and-computational-approaches-fall-2017/segments/6202?summary
Our course textbook is Strogatz's book on chaos which is a great resource: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536 . I believe he also has a lectures series out on Youtube.