Interesting recurrence equation models?

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So I've had an introductory subject to recurrence equations and now I have to study a model using recurrence equations as a project. The problem is that most models I find are either elemental or precisely those I've already studied (dynamic of population up to logistic model, Fibonacci sequence, etc). It would be really useful if someone who studied the subject and found interesting models easy enough for a short project could point them out to me.

Thank you!