{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T17:03:58Z","timestamp":1782493438674,"version":"3.54.5"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T00:00:00Z","timestamp":1478649600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/systems4040034","type":"journal-article","created":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T10:09:39Z","timestamp":1478686179000},"page":"34","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Emergence at the Fundamental Systems Level: Existence Conditions for Iterative Specifications"],"prefix":"10.3390","volume":"4","author":[{"given":"Bernard","family":"Zeigler","sequence":"first","affiliation":[{"name":"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Muzy","sequence":"additional","affiliation":[{"name":"CNRS, I3S, Universit\u00e9 C\u00f4te d\u2019Azur, 06900 Sophia Antipolis, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.cogsys.2012.06.003","article-title":"Emergence in stigmergic and complex adaptive systems: A formal discrete event systems perspective","volume":"21","author":"Mittal","year":"2013","journal-title":"Cogn. Syst. Res."},{"key":"ref_2","unstructured":"Mittal, S., and Rainey, L. (2015, January 26\u201329). Harnessing emergence: The control and design of emergent behavior in system of systems engineering. Proceedings of the Conference on Summer Computer Simulation, SummerSim\u201915, Chicago, IL, USA."},{"key":"ref_3","unstructured":"Ashby, W. (1964). An Introduction to Cybernetics, University Paperbacks."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/03081078508934879","article-title":"Emergence and computation","volume":"10","author":"Foo","year":"1985","journal-title":"Int. J. Gen. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1162\/106454603321489518","article-title":"Toward a formalization of emergence","volume":"9","author":"Kubik","year":"2003","journal-title":"Artif. Life"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6:1","DOI":"10.1145\/2815502","article-title":"Formalization of weakemergence in multiagent systems","volume":"26","author":"Szabo","year":"2015","journal-title":"ACM Trans. Model. Comput. Simul."},{"key":"ref_7","first-page":"1033","article-title":"System Theoretic Foundations of Modeling and Simulation: A Historic Perspective and the Legacy of A. Wayne Wymore","volume":"88","author":"Zeigler","year":"2012","journal-title":"Simul. Trans. Soc. Model. Simul."},{"key":"ref_8","unstructured":"Zeigler, B., and Muzy, A. (2016, January 23\u201326). Some Modeling & Simulation Perspectives on Emergence in System-of-Systems. Proceedings of the SpringSim2016, Virginia Beach, VA, USA."},{"key":"ref_9","unstructured":"Wikipedia. Available online: https:\/\/en.wikipedia.org\/wiki\/Turing_machine."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1145\/384169.384173","article-title":"Dynamic structures in modeling and simulation: A reactive approach","volume":"11","author":"Uhrmacher","year":"2001","journal-title":"ACM Trans. Model. Comput. Simul."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Nutaro, J. (2011). Building Software for Simulation: Theory and Algorithms with Applications in C++, Wiley.","DOI":"10.1002\/9780470877999"},{"key":"ref_12","unstructured":"Zeigler, B., Praehofer, H., and Kim, T. (2000). Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems, Academic Press."},{"key":"ref_13","unstructured":"Giambiasi, N., Escude, B., and Ghosh, S. (2001, January 26\u201328). GDEVS: A generalized discrete event specification for accurate modeling of dynamic systems. Proceedings of the Autonomous Decentralized Systems, Dallas, TX, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1177\/0037549702078001198","article-title":"Modeling and Simulation of Dynamic Structure Heterogeneous Flow Systems","volume":"78","author":"Barros","year":"2002","journal-title":"SIMULATION Trans. Soc. Model. Simul. Int."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1145\/937332.937335","article-title":"Dynamic Structure Multi-Paradigm Modeling and Simulation","volume":"13","author":"Barros","year":"2003","journal-title":"ACM Trans. Model. Comput. Simul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9:1","DOI":"10.1145\/2818641","article-title":"Intensional couplings in variable-structure models: An exploration based on multilevel-DEVS","volume":"26","author":"Steiniger","year":"2016","journal-title":"ACM Trans. Model. Comput. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1450012","DOI":"10.1142\/S1793962314500123","article-title":"Specification of dynamic structure discrete event systems using single point encapsulated control functions","volume":"5","author":"Muzy","year":"2014","journal-title":"Int. J. Model. Simul. Sci. 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