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Synchronized family dynamics in globally coupled maps.

N. J. Balmforth1, A. Jacobson, A. Provenzale

  • 1Scripps Institution of Oceanography, University of California, La Jolla, California 92093Istituto di Cosmogeofisica, C. Fiume 4, 10133 Torino, Italy.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary
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This study classifies solutions for globally coupled logistic map lattices. It reveals synchronized states, chaotic asynchronous lattices, and partitioned synchronized families, particularly detailing two-family states.

Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Statistical physics

Background:

  • Globally coupled logistic map lattices exhibit complex behaviors.
  • Understanding their dynamics is crucial for complex systems research.

Purpose of the Study:

  • To explore the dynamics of globally coupled logistic map lattices.
  • To classify solution phenomenology across a parameter plane.
  • To detail the dynamics and stability of two-family states.

Main Methods:

  • Exploration of parameter plane (coupling strength, epsilon, and map parameter, a).
  • Analysis of simple periodic orbits in small lattices.
  • Extensive initial-value calculations.

Main Results:

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  • Lattices exhibit stable solutions, except for high coupling (synchronization) or low map parameters (fixed points).
  • Chaotic, asynchronous lattices found for smaller epsilon and larger a.
  • Most states partition into synchronized families, with two-family states explored in detail.

Conclusions:

  • The parameter plane reveals diverse dynamic regimes.
  • Synchronized states and partitioned families are common outcomes.
  • Two-family states present a significant area for further dynamic and stability analysis.