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

Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada Kobe 657-8501, Japan.
Biosystems (Impact Factor: 1.55). 02/2008; 91(1):13-33. DOI: 10.1016/j.biosystems.2007.06.005
Source: PubMed


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.

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