CML and driven IFS

To look for evidence of synchronizaton in the average of coupled logistic maps, we use the driven IFS. If any of these looks like the IFS driven by a single logistic map, we will investigate in more detail.

We simplify the general network to this

xn+1 = (1 - c) ⋅ 4 ⋅ xn(1 - xn) + c ⋅ 4 ⋅ yn(1 - yn) yn+1 = (1 - c) ⋅ 4 ⋅ yn(1 - yn) + c ⋅ 4 ⋅ xn(1 - xn)

so c = 0 is the uncoupled system.

For comparison, the IFS driven by a single s = 4 logistic map is shown on the right.

c=0.0 c=0.1 c=0.2 c=0.3 c=0.4 c=0.5 c=0.6 c=0.7 c=0.8 c=0.9 c=1.0 animate