Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Complex arithmetic and quaternion arithmetic Next Document: Feigenbaum's constant See reader questions & answers on this topic!  Help others by sharing your knowledge Q9: What is the logistic equation? A9: It models animal populations. The equation is x > c*x*(1x), 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. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Complex arithmetic and quaternion arithmetic Next Document: Feigenbaum's constant Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: stepp@marshall.edu
Last Update March 27 2014 @ 02:11 PM
