Zeigler, B.P.; Muzy, A. Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications. Systems2016, 4, 34.
Zeigler, B.P.; Muzy, A. Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications. Systems 2016, 4, 34.
Zeigler, B.P.; Muzy, A. Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications. Systems2016, 4, 34.
Zeigler, B.P.; Muzy, A. Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications. Systems 2016, 4, 34.
Abstract
Conditions under which compositions of component systems form a well-defined system-of-systems here are 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.
Keywords
emergence; uniqueness; existence of solutions; input/output system; system specifications; discrete event system specification
Subject
Computer Science and Mathematics, Computer Science
Copyright:
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.
