Coupled Map Lattice
A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems (especially partial differential equations). They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems. This includes the dynamics of spatiotemporal chaos where the number of effective degrees of freedom diverges as the size of the system increases.
Features of the CML are discrete time dynamics, discrete underlying spaces (lattices or networks), and real (number or vector), local, continuous state variables. Studied systems include populations, chemical reactions, convection, fluid flow and biological networks. More recently, CMLs have been applied to computational networks identifying detrimental attack methods and cascading failures.
CML’s are comparable to cellular automata models in terms of their discrete features. However, the value of each site in a cellular automata network is strictly dependent on its neighbor (s) from the previous time step. Each site of the CML is only dependent upon its neighbors relative to the coupling term in the recurrence equation. However, the similarities can be compounded when considering multi-component dynamical systems.
Famous quotes containing the words coupled and/or map:
“That is coupled to foul thraldom.
But if he had assayed it,
Then all perquer he should it wit;
And should think freedom more to prize
Than all the gold in world that is.”
—John Barbour (1316?1395)
“You can always tell a Midwestern couple in Europe because they will be standing in the middle of a busy intersection looking at a wind-blown map and arguing over which way is west. European cities, with their wandering streets and undisciplined alleys, drive Midwesterners practically insane.”
—Bill Bryson (b. 1951)