Deterministic Chaos

Tent Map

The Tent Map is one of the simplest nonlinear functions. It consists of two linear functions:
T(x) = s⋅x for x ≤ 1/2
T(x) = s⋅(1-x) for x ≥ 1/2
For small x, the Tent Map represents growth; for larger x decline, perhaps an effect of competition for limited resources.
Note the maximum value occurs at x = 1/2, and that maximum value is s/2.
We shall see the graph should stay inside the unit square. Consequently, we restrict the number s to the range
0 ≤ s ≤ 2.
We shall see that as s varies, the structure of the orbit x0, x1 = T(x0), x2 = T(x1), ... varies in a very complicated way, but not as complicated as that of the logistic map.
Nevertheless, the iterates of the tent map exhibit rich behavior, including chaos.

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