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-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of brian
whatcott
Sent: Wednesday, April 18, 2018 11:29 PM
To: prefered phys-l address <phys-l@phys-l.org>
Subject: [Phys-L] Rodent Population Model Behavior.
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.
https://imgur.com/a/63jox
Enjoy!
Brian W
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