Exponential and logistic growth
February 2018
Alligood, Sauer, and Yorke (1997) in their book present models for exponential and logistic growth. I visualised both with short Octave functions.

Exponential growth

The model

f(x) = 2x


applied recursively with x = 0.01 and 12 iterations:




function exponential_growth(x, n, v)
g = 2 * x;
n -= 1;
v = [v g];

if n == 0
plot(1:length(v), v, "linewidth", 2)
break
endif

exponential_growth(g, n, v);
endfunction


Logistic growth

The model

g(x) = 2x(1 - x)


applied recursively with x = 0.01 and 12 iterations:




function logistic_growth(x, n, v)
g = 2 * x * (1 - x);
n -= 1;
v = [v g];

if n == 0
plot(1:length(v), v, "linewidth", 2)
break
endif

logistic_growth(g, n, v);
endfunction


[1] Alligood, Kathleen T. & Sauer, Tim D. & Yorke, James A. (1997). Chaos: An Introduction to Dynamical Systems. New York: Springer. ISBN: 0-387-94677-2.