How common is chaos?

Logistic Map

xn+1 = Axn(1 - xn)

-2

4

A

Lyapunov Exponent

1

-1

Previous slide

Next slide

Back to first slide

View graphic version

Simplest 1-D chaotic system

Chaotic over 13% of the range of A

Solutions are unbounded outside the range plotted (hence unphysical)