Logistic map

From InterSciWiki

http://hornacek.coa.edu/dave/Chaos/

Wikipedia:Logistic_map#Chaos_and_the_logistic_map, modeling for example, reproduction and starvation (density-dependent mortality), and the deep link between chaos and fractals. Mathematically, the logistic map is written

$(1)\qquad x_{n+1} = r x_n (1-x_n)$

where:

x n

is a number between zero and one, and represents the population at year n, and hence x₀ represents the initial population (at year 0)

r is a positive number, and represents a combined rate for reproduction and starvation.

The Wikipedia:logistic function is the solution of the simple first-order non-linear Wikipedia:differential equation having the logistic map property:

$\frac{dP}{dt}=P(1-P) \!$