Abstract heterarchy: Time/state-scale re-entrant form

Yukio Pegio Gunji, Kazauto Sasai, Sohei Wakisaka

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A heterarchy is a dynamical hierarchical system inheriting logical inconsistencies between levels. Because of these inconsistencies, it is very difficult to formalize a heterarchy as a dynamical system. Here, the essence of a heterarchy is proposed as a pair of the property of self-reference and the property of a frame problem interacting with each other. The coupling of them embodies a one-ity inheriting logical inconsistency. The property of self-reference and a frame problem are defined in terms of logical operations, and are replaced by two kinds of dynamical system, temporal dynamics and state-scale dynamics derived from the same "liar statement". A modified tent map serving as the temporal dynamics is twisted and coupled with a tent map serving as the state-scale dynamics, and this results in a discontinuous self-similar map as a dynamical system. This reveals that the state-scale and temporal dynamics attribute to the system, and shows both robust and emergent behaviors.

Original languageEnglish
Pages (from-to)13-33
Number of pages21
JournalBioSystems
Volume91
Issue number1
DOIs
Publication statusPublished - 2008 Jan 1
Externally publishedYes

Keywords

  • Chaotic liar
  • Frame problem
  • Heterarchy
  • Self-reference
  • Self-similar map

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics

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