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Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications

Conditions under which compositions of component systems form a well-defined system-of-systems are here formulated at a fundamental level. Statement of what defines a well-defined composition and sufficient conditions guaranteeing such a result offers insight into exemplars that can be found in special cases such as differential equation and discrete event systems. For any given global state of a composition, two requirements can be stated informally as: (1) the system can leave this state, i.e., there is at least one trajectory defined that starts from the state; and (2) the trajectory evolves over time without getting stuck at a point in time. Considered for every global state, these conditions determine whether the resultant is a well-defined system and, if so, whether it is non-deterministic or deterministic. We formulate these questions within the framework of iterative specifications for mathematical system models that are shown to be behaviorally equivalent to the Discrete Event System Specification (DEVS) formalism. This formalization supports definitions and proofs of the afore-mentioned conditions. Implications are drawn at the fundamental level of existence where the emergence of a system from an assemblage of components can be characterized. We focus on systems with feedback coupling where existence and uniqueness of solutions is problematic.

Identiferoai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/622817
Date09 November 2016
CreatorsZeigler, Bernard, Muzy, Alexandre
ContributorsUniv Arizona, ACIMS
PublisherMDPI AG
Source SetsUniversity of Arizona
LanguageEnglish
Detected LanguageEnglish
TypeArticle
Rights© 2016 by the authors; licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Relationhttp://www.mdpi.com/2079-8954/4/4/34

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