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). |
See also
Quick quiz
Test yourself on coupled-logistic
8 multiple-choice questions. Pick an answer for each, then submit to see explanations.
Q1.A coupled-map lattice (CML) is:
Q2.What new phenomenon do CMLs show that single maps cannot?
Q3.Kunihiko Kaneko introduced CMLs in:
Q4.The coupling strength ε in a CML is typically:
Q5.Kaneko's phase diagram classifies CML phases including:
Q6.Globally coupled maps (GCMs) differ from CMLs by:
Q7.Real systems modelled by CMLs include:
Q8.The Lyapunov spectrum of a CML scales how with lattice size N?