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
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