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Fractal Frequently Asked Questions and Answers
Section - Logistic equation

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Q9: What is the logistic equation?  
A9: It models animal populations. The equation is x -> c*x*(1-x), where x  
is the population (between 0 and 1) and c is a growth constant. Iteration of  
this equation yields the period doubling route to chaos. For c between  
1 and 3, the population will settle to a fixed value. At 3, the period 
doubles to 2; one year the population is very high, causing a low population
the next year, causing a high population the following year. At 3.45, the
period  doubles again to 4, meaning the population has a four year cycle. 
The period keeps doubling, faster and faster, at 3.54, 3.564, 3.569, and 
so forth.  At 3.57, chaos occurs; the population never settles to a fixed 
period. For most c values between 3.57 and 4, the population is chaotic, 
but there are also periodic regions. For any fixed period, there is some 
c value that will yield that period. See "An Introduction to Chaotic 
Dynamical Systems" for more information.  
  

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Top Document: Fractal Frequently Asked Questions and Answers
Previous Document: Complex arithmetic and quaternion arithmetic
Next Document: Feigenbaum's constant

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Last Update March 27 2014 @ 02:11 PM