Douglas J. Ingalls
1934 - 1999
One of the more simpler equations in chaos is the logistics equation. The logistic equation, y = b*x*(1-x), may be written in a more generalized form as y = a*x + b*x*(1-x). The addition of the leading term may be thought of as a migration term. If part of the population is removed this would correspond to an emigration. If part of the population is increased this would correspond to an immigration. Both of these cases are of interest and extend the knowledge of the properties of the original equation.
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The logistic equation with emigration of -1.0
The logistic equation with emigration of -0.5
The logistic equation with no migration (classic)
The logistic equation with immigration of 0.5
The logistic equation with immigration of 1.0
Gallery of graphs for the above cases
Table of results for the above cases
QBASIC program for studying the equation
Some issues in convergence
References to the logistic equations
next Introduction to the generalized equation
Revised 10 September 1996
Modified 16 Sep 2007
