{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T10:37:40Z","timestamp":1776076660091,"version":"3.50.1"},"reference-count":12,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T00:00:00Z","timestamp":1490918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010751","name":"FONDECYT","doi-asserted-by":"publisher","award":["1150229"],"award-info":[{"award-number":["1150229"]}],"id":[{"id":"10.13039\/501100010751","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010751","name":"FONDECYT","doi-asserted-by":"publisher","award":["3170122"],"award-info":[{"award-number":["3170122"]}],"id":[{"id":"10.13039\/501100010751","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Reaction Networks have been recently proposed as a framework for systems modeling due to its capability to describe many entities interacting in contextual ways and leading to the emergence of meta-structures. Since systems can be subjected to structural changes that not only alter their inner functioning, but also their underlying ontological features, a crucial issue is how to address these structural changes within a formal representational framework. When modeling systems using reaction networks, we find that three fundamentally different types of structural change are possible. The first corresponds to the usual notion of perturbation in dynamical systems, i.e., change in system\u2019s state. The second corresponds to behavioral changes, i.e., changes not in the state of the system but on the properties of its behavioral rules. The third corresponds to radical structural changes, i.e., changes in the state-set structure and\/or in reaction-set structure. In this article, we describe in detail the three types of structural changes that can occur in a reaction network, and how these changes relate to changes in the systems observable within this reaction network. In particular, we develop a decomposition theorem to partition a reaction network as a collection of dynamically independent modules, and show how such decomposition allows for precisely identifying the parts of the reaction network that are affected by a structural change.<\/jats:p>","DOI":"10.3390\/systems5020030","type":"journal-article","created":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T10:35:49Z","timestamp":1490956549000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Reaction Networks as a Language for Systemic Modeling: On the Study of Structural Changes"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3014-8340","authenticated-orcid":false,"given":"Tomas","family":"Veloz","sequence":"first","affiliation":[{"name":"Center Leo Apostel, Brussels Free University, 1050 Brussels, Belgium;"},{"name":"Insituto de Filosof\u00eda y Ciencias de la Complejidad, Los Alerces 3024, \u00d1u\u00f1oa, Chile;"}]},{"given":"Pablo","family":"Razeto-Barry","sequence":"additional","affiliation":[{"name":"Insituto de Filosof\u00eda y Ciencias de la Complejidad, Los Alerces 3024, \u00d1u\u00f1oa, Chile;"},{"name":"Vicerrector\u00eda Acadm\u00b4 ica, Universidad Diego Portales, Manuel Rodrg\u00b4uez Sur 415, Santiago, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,31]]},"reference":[{"key":"ref_1","unstructured":"Vemuri, V. (2014). Modeling of Complex Systems: An Introduction, Academic Press."},{"key":"ref_2","unstructured":"Strogatz, S.H. (2014). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0370-1573(99)00096-4","article-title":"The control of chaos: Theory and applications","volume":"329","author":"Boccaletti","year":"2000","journal-title":"Phys. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/S0020-7373(75)80015-0","article-title":"The organization of the living: A theory of the living organization","volume":"7","author":"Maturana","year":"1975","journal-title":"Int. J. Man-Mach. Stud."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Licata, I., and Minati, G. (2016). Emergence, computation and the freedom degree loss information principle in complex systems. Found. Sci.","DOI":"10.1007\/s10699-016-9503-x"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Veloz, T., and Razeto-Barry, P. (2017). Reaction networks as a language for systemic modeling: Fundamentals and examples. Systems, 5.","DOI":"10.3390\/systems5010011"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1007\/s11538-006-9130-8","article-title":"Chemical organisation theory","volume":"69","author":"Dittrich","year":"2007","journal-title":"Bull. Math. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1142\/S0219525911002895","article-title":"On the relation between organizations and limit sets in chemical reaction systems","volume":"14","author":"Peter","year":"2011","journal-title":"Adv. Complex Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Peter, S., Veloz, T., and Dittrich, P. (2010, January 24\u201327). Feasibility of organizations-a refinement of chemical organization theory with application to p systems. Proceedings of the Eleventh International Conference on Membrane Computing (CMC11), Jena, Germany.","DOI":"10.1007\/978-3-642-18123-8_25"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"i475","DOI":"10.1093\/bioinformatics\/btu453","article-title":"Effects of small particle numbers on long-term behaviour in discrete biochemical systems","volume":"30","author":"Kreyssig","year":"2014","journal-title":"Bioinformatics"},{"key":"ref_11","unstructured":"Veloz, T., Reynaert, B., Rojas, D., and Dittrich, P. (2011, January 8\u201312). A decomposition Theorem in chemical organizations. Proceedings of the European Conference in Artificial Life\u2014ECAL, Paris, France."},{"key":"ref_12","unstructured":"Strang, G. (2011). Introduction to Linear Algebra, Wellesley-Cambridge Press."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/5\/2\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:31:43Z","timestamp":1760207503000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/5\/2\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":12,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,6]]}},"alternative-id":["systems5020030"],"URL":"https:\/\/doi.org\/10.3390\/systems5020030","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,31]]}}}