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Systems 2016, 4(4), 34; doi:10.3390/systems4040034

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

1
Co-Director of the Arizona Center for Integrative Modeling and Simulation (ACIMS), University of Arizona and Chief Scientist, RTSync Corp. 12500 Park Potomac Ave. #905-S, Potomac, MD 20854, USA
2
CNRS, I3S, Université Côte d’Azur, 06900 Sophia Antipolis, France
*
Author to whom correspondence should be addressed.
Academic Editors: Gianfranco Minati, Eliano Pessa and Ignazio Licata
Received: 17 August 2016 / Revised: 30 September 2016 / Accepted: 25 October 2016 / Published: 9 November 2016
View Full-Text   |   Download PDF [482 KB, uploaded 9 November 2016]   |  

Abstract

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. View Full-Text
Keywords: emergence; uniqueness; existence of solutions; input/output system; system specifications; Discrete Event System Specification emergence; uniqueness; existence of solutions; input/output system; system specifications; Discrete Event System Specification
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MDPI and ACS Style

Zeigler, B.P.; Muzy, A. Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications. Systems 2016, 4, 34.

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