The following discrete-time dynamical systems have slope of exactly -1 at the equilibrium. Check this, and then

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The following discrete-time dynamical systems have slope of exactly -1 at the equilibrium. Check this, and then iterate the function for a few steps starting from near the equilibrium to see whether it is stable, unstable, or neither.
xt + 1 = 3xt (1 - xt), the logistic system with r = 3.
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