Coupled Map Lattices: at the Age of Maturity

  • L.A. Bunimovich
Part of the Lecture Notes in Physics book series (LNP, volume 671)


Coupled Map Lattices (CML) were simultaneously and independently introduced by K. Kaneko, R. Kapral and S. Kuznetsov in 1983–84 [1, 2, 3, 4, 5, 6]. CML describe the time evolution of fields that can be split into an independent evolution of local systems (elements) of these fields (usually defined by some map of a local phase space) followed by (spatial) interactions of these local systems generated by some operator acting on the entire (global) phase space of CML. A structure of local systems in CML forms a lattice. At any moment of time all values of local variables are defined. These values determine a spatial structure (pattern) of the field. In CML it is assumed that all local dynamical systems are identical and that the spatial interactions between any local system and the rest of CML are the same for all local systems. (In more general Lattice Dynamical Systems (LDS) dynamics is not assumed to be a composition of a local dynamics and spatial interactions and neither to be translationally invariant.)


Invariant Measure Coherent Structure Local System Local Dynamic Spatial Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Authors and Affiliations

  • L.A. Bunimovich
    • 1
  1. 1.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA

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