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Re: [Phys-L] Rodent Population Model Behavior.



This is also explored as a computer simulation by Gould & Tobochnik in Part 1 of An Introduction to Computer Simulation Methods: Applications to Physical Systems. It's out of print now, but the PDF of the 3rd edition is downloadable from COMPADRE.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of Don via Phys-l
Sent: Thursday, April 19, 2018 3:47 PM
To: Phys-L@Phys-L.org
Cc: Don <dgpolvani@gmail.com>
Subject: Re: [Phys-L] Rodent Population Model Behavior.

Thanks for posting this. I enjoy playing with such equations. As you pointed out, for something so simple looking, the equation has a complicated behavior depending on its parameters. I've seen this model also called the logistic difference equation. Note R must be > 0 since values of R = 0 will cause all future X' to be zero for any initial X. Similarly, the initial X must be > 0, since initial X = 0 results in all future X' = 0 for any R.

Don
Dr. Donald G. Polvani
Adjunct Faculty, Physics, Retired
Anne Arundel Community College

-----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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