Discrete map · Coupled · dim 2
Coupled logistic / CML
A coupled map lattice (CML). The same logistic dynamics happens at every site of a 1D lattice, with weak diffusive coupling to neighbours. Produces spatiotemporal chaos, travelling waves, and pattern formation.
Equations
x_{n+1}^{i} = (1 − ε) f(x_n^i) + (ε/2) (f(x_n^{i−1}) + f(x_n^{i+1}))
f(x) = r x (1 − x)At a glance
| Parameters | r, ε, lattice size N |
|---|---|
| Chaotic for | r > r∞ ≈ 3.57; coupling ε determines spatial structure |
| History | Kunihiko Kaneko (1984). |