Definition:Logistic Map

Not to be confused with Definition:Logistic Function.

Definition

The logistic map is an iterated mapping defined on the closed unit interval $\closedint 0 1$ as:

$x_{n + 1} = a x_n \paren {1 - x_n}$

where:

$x_0$ can be anywhere in $\openint 0 1$

$a$ is a real constant in the interval $\hointl 0 4$.

Parameter

The real constant $a$ is known as the parameter.

Also see

• Nature of Logistic Map for Various Parameter Values

• Results about the logistic map can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logistic map
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logistic map