Mathematics of symmetry in chaos

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I'm a neuroscience PhD student. Recently I became so interested in the mathematical equations involving order and disorder and complex plane. I read a book named "Symmetry in chaos" by Martin Golubitsky. It's about the generation of symmetrical patterns using simple chaotic equations based like this equation

I'm really willing to learn about the mathematics of this kind, to understand what is done here because it's so related to my field and I just know some calculus, so I ask from you great guys to guide me by either introducing some books or teaching me directly. Actually I would love to have a remote advanced math teacher and I'm willing to pay for the services. Thanks.