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I don't want to list the exact problem I have to solve, as I would rather do it myself, all I would like is some guidance. The problem is a function like: P_{k+1}=a (P_{k}-1) with a few more constants and some brackets thrown about on the right hand side. I need to find all the equilibrium points. I am not exactly sure how to get started, and I have had a look in my textbook and couldn't find any examples similar to this. Do I just derive this function, and then let it equal zero to solve for the points?

Also, when I expand the function I will have a polynomial with P_{k}^3, so there will be multiple solutions I assume.

Thanks for the help!

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# Equilibrium solutions in mathematical modelling

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