**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.