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Coupled map lattices as computational systems.

A. V. Holden1, J. V. Tucker, H. Zhang

  • 1Department of Physiology, University of Leeds, Leeds LS2 9JT, United KingdomDepartment of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, United KingdomDepartment of Physiology, University of Leeds, Leeds LS2 9JT, United KingdomDepartment of Mathematics and Computer Science, University College of Swansea, Swansea SA2 8PP, United Kingdom.

Chaos (Woodbury, N.Y.)
|July 1, 1992
PubMed
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The coupled map lattice (CML) offers a new parallel computing model. However, CML computers cannot perform computations beyond standard real number models.

Area of Science:

  • Computational theory
  • Mathematical physics

Background:

  • Coupled map lattices (CML) are discrete dynamical systems.
  • The computational capabilities of CMLs are not fully understood.

Purpose of the Study:

  • To evaluate the coupled map lattice (CML) as a mathematical model for computation.
  • To determine if CML computers offer novel computational power compared to existing models.

Main Methods:

  • Utilizing the theory of synchronous concurrent algorithms.
  • Developing new general mathematical definitions for CMLs.
  • Employing an axiomatic approach to analyze CML computability.

Main Results:

  • The coupled map lattice (CML) is a valid model for parallel deterministic analog computation.

Related Experiment Videos

  • CML computers do not possess computational capabilities exceeding standard real number computation models.
  • New mathematical definitions and an axiomatic framework for CML analysis were established.

    • Conclusions:

    • Coupled map lattices (CML) represent a valid, albeit not superior, model for parallel analog computing.
    • The computational scope of CMLs is theoretically bounded by existing real number computation paradigms.
    • This study provides a rigorous mathematical foundation for understanding CML computability.