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Comment II on "Simple measure for complexity"

Binder1, Perry

  • 1Departamento de Fisica, Universidad de Los Andes, Apartado Aereo 4976, Bogota, Colombia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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A recently proposed complexity measure fails to capture the language transition in quadratic maps. This study highlights a general limitation of this complexity measure for dynamical systems.

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Information Theory and Complexity

Background:

  • The transition from regular to indexed languages is a key feature in the dynamics of certain systems.
  • A complexity measure by Shiner, Davidson, and Landsberg was proposed to quantify such transitions.

Purpose of the Study:

  • To evaluate the adequacy of the Shiner, Davidson, and Landsberg complexity measure.
  • To identify limitations in describing language transitions at period-doubling accumulation points.

Main Methods:

  • Analysis of language transitions in quadratic maps.
  • Critique of the Shiner, Davidson, and Landsberg complexity measure.

Main Results:

  • The proposed complexity measure does not accurately describe the observed language transitions.

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  • The measure exhibits generic inadequacy in characterizing these dynamical system phenomena.

    • Conclusions:

    • The Shiner, Davidson, and Landsberg complexity measure is insufficient for understanding period-doubling bifurcations in quadratic maps.
    • Further development of complexity measures is needed for dynamical systems exhibiting complex language transitions.