Chaos Lab

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.

Coupled-map lattice (logistic, ε = 0.3, r = 3.97). x-axis = lattice site, y-axis = time. Spatiotemporal chaos.

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

Parametersr, ε, lattice size N
Chaotic forr > r∞ ≈ 3.57; coupling ε determines spatial structure
HistoryKunihiko Kaneko (1984).

See also

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