History
CMLs were first introduced in the mid 1980’s through a series of closely released publications. Kapral used CMLs for modeling chemical spatial phenomena. Kuznetsov sought to apply CMLs to electrical circuitry by developing a renormalization group approach (similar to Feigenbaum's universality to spatially extended systems). Kaneko's focus was more broad and he is still known as the most active researcher in this area. The most examined CML model was introduced by Kaneko in 1983 where the recurrence equation is as follows:
where and is a real mapping.
The applied CML strategy was as follows:
- Choose a set of field variables on the lattice at a macroscopic level. The dimension (not limited by the CML system) should be chosen to correspond to the physical space being researched.
- Decompose the process (underlying the phenomena) into independent components.
- Replace each component by a nonlinear transformation of field variables on each lattice point and the coupling term on suitable, chosen neighbors.
- Carry out each unit dynamics ("procedure") successively.
Read more about this topic: Coupled Map Lattice
Famous quotes containing the word history:
“History is the present. That’s why every generation writes it anew. But what most people think of as history is its end product, myth.”
—E.L. (Edgar Lawrence)
“Certainly there is not the fight recorded in Concord history, at least, if in the history of America, that will bear a moment’s comparison with this, whether for the numbers engaged in it, or for the patriotism and heroism displayed.”
—Henry David Thoreau (1817–1862)
“As History stands, it is a sort of Chinese Play, without end and without lesson.”
—Henry Brooks Adams (1838–1918)