Bifurcation Diagram for the Tent Map

n

100

x

0

0.4

r

1.2

The tent map is a piecewise linear, one-dimensional map

x↦rmin(x,1-x)

. Like the logistic map, its iterates exhibit chaotic dynamics for a range of values of the parameter

r

. The plot at the top shows the orbit after

n

steps for an initial value

x

0

and a particular value of

r

.

The iterated map is

x

n+1

=

r x n	x n <0.5
r(1- x n )	x n ≥0.5

with

1≤r≤2

.

[1] Wikipedia. "Tent Map." (March 6, 2013) en.wikipedia.org/wiki/Tent_map.

Enrique Zeleny