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I have been given a difference equation: $x_{t+1} = a\cdot x_t\cdot(1-x_t)$ and I want to find out the equilibrium points of the system. Could you recommend something to read in order to solve this problem?

The only thing I would know is to set $x_{t+1}= x_t$.

How do I solve this ? :(

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    May I suggest that someone promote a comment to an answer? Brian, Ross, Andre?2011-10-04

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$x=ax(1−x)$, or equivalently $ax^2−(a−1)x=0$, with the solutions $x=0$ and $x=(a−1)/a\ $ (if $a≠0$)

Thanks @André Nicolas and @Ross Millikan