Finding Strange Attractors of Iterated Maps

polynomial degree of the iterated map

2

3

4

5

find another attractor

This Demonstration searches for strange attractors of a nonlinear two-dimensional polynomial map. Both the

x

and the

y

polynomial maps of degree

n

are defined by

1

2

(n+1)(n+2)

coefficients

c

ij

, one for each term

i

x

j

y

,

i,j=0,1,…,n

,

i+j≤n

.

To find an attractor, we compare two orbits of the map with the same coefficients but starting from nearby initial points. If the orbits become unbounded or move apart, another set of random coefficients is selected. If successive iterations move the orbits increasingly closer together, an attractor is detected and plotted and the search is stopped.