I looked over a used book sale at the local library last week. I chose
just one book: "A Mathematician Reads The Newspaper" (BasicBooks 1995)
My interest was captured by a little piece on a population dynamics
model explored by May & Feigenbaum. The iterative model they used was
indeed simple - a logistic curve generator: X' = R * X ( 1 - X )
X' next year's normalized population.
X this year's normalized population [0..1]
R is a parameter [0..4]
Examples: for X = 0.1 and R = 1.5 The population stabilizes at 0.333
after some years. This steady state population is invariant to the
starting X value.
When R = 3.2 the population alternates between two values:
when R = 3.5 the population steps between four values;
Slightly larger R values continue to double the number of population
states until R = 3.57 when the population size becomes chaotic.