Abstract heterarchy: time/state-scale re-entrant form.
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.
Gunji
Yukio-Pegio
YP
Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada Kobe 657-8501, Japan. yukio@kobe-u.ac.jp
Sasai
Kazauto
K
Wakisaka
Sohei
S
D003198:Computer Simulation; D008954:Models, Biological; D013997:Time Factors