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Coupled trivial maps.

L. A. Bunimovich1, R. Livi, G. Martinez-Mekler

  • 1Georgia Institute of Technology, School of Mathematics, Atlanta, Georgia 30332Institute of Oceanology, Russian Academy of Science, 117218 Moscow, RussiaDipartimento di Fisica, Universita di Firenze, Largo E. Fermi 2, 50125 Firenze, ItalyINFN and INFM Sezione di FirenzeInstituto de Fisica, UNAM, Apdo. Postal 20-364, 01000 Mexico D.F., MexicoDipartimento di Energetica, Universita di Firenze, Firenze, ItalyINFN and INFM Sezione di Firenze.

Chaos (Woodbury, N.Y.)
|July 1, 1992
PubMed
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This study introduces a novel coupled map lattice model rigorously analyzed across all interaction strengths. The model features one-dimensional maps with stable periodic orbits and nearest-neighbor diffusive coupling.

Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Mathematical Physics

Background:

  • Coupled map lattices (CMLs) are crucial models for studying spatio-temporal chaos.
  • Rigorous analysis of CMLs across the full range of interaction strengths remains challenging.
  • Existing models often lack comprehensive analytical tractability.

Purpose of the Study:

  • To present the first nontrivial example of coupled map lattices amenable to rigorous analysis.
  • To investigate CMLs with a specific class of one-dimensional maps and diffusive coupling.
  • To establish a theoretical framework for understanding complex dynamics in coupled systems.

Main Methods:

  • Consideration of one-dimensional maps possessing a globally attracting superstable periodic trajectory.

Related Experiment Videos

  • Application of diffusive nearest-neighbor interaction for coupling the maps.
  • Development of analytical techniques to cover the entire spectrum of interaction strengths.

    • Main Results:

    • A novel class of coupled map lattices is rigorously analyzed.
    • The analysis spans the complete range of spatial interaction strengths.
    • The model demonstrates complex dynamical behaviors arising from the interplay of local dynamics and coupling.

    Conclusions:

    • The introduced CML model provides a tractable framework for studying complex systems.
    • This work advances the theoretical understanding of spatio-temporal dynamics in coupled systems.
    • The findings pave the way for analyzing more complex lattice models.