Editing Complex system (section)

== Applications ==

===Complexity in practice===
The traditional approach to dealing with complexity is to reduce or constrain it. Typically, this involves compartmentalization: dividing a large system into separate parts. Organizations, for instance, divide their work into departments that each deal with separate issues. Engineering systems are often designed using modular components. However, modular designs become susceptible to failure when issues arise that bridge the divisions.

===Complexity of cities===
Jane Jacobs described cities as being a problem in organized complexity in 1961, citing Dr. Weaver's 1948 essay.<ref>{{cite book |last1=Jacobs |first1=Jane |title=The Death and Life of Great American Cities |date=1961 |publisher=Vintage Books |location=New York |pages=428–448}}</ref> As an example, she explains how an abundance of factors interplay into how various urban spaces lead to a diversity of interactions, and how changing those factors can change how the space is used, and how well the space supports the functions of the city. She further illustrates how cities have been severely damaged when approached as a problem in simplicity by replacing organized complexity with simple and predictable spaces, such as Le Corbusier's "Radiant City" and Ebenezer Howard's "Garden City". Since then, others have written at length on the complexity of cities.<ref>{{cite web |title=Cities, scaling, & sustainability |url=https://www.santafe.edu/research/projects/cities-scaling-sustainability |publisher=Santa Fe Institute |access-date=28 October 2023}}</ref>

===Complexity economics===
Over the last decades, within the emerging field of [[complexity economics]], new predictive tools have been developed to explain economic growth. Such is the case with the models built by the [[Santa Fe Institute]] in 1989 and the more recent [[economic complexity index]] (ECI), introduced by the [[MIT]] physicist [[Cesar A. Hidalgo]] and the [[Harvard]] economist [[Ricardo Hausmann]].

[[Recurrence quantification analysis]] has been employed to detect the characteristic of [[business cycles]] and [[economic development]]. To this end, Orlando et al.<ref>{{Cite journal |last1=Orlando |first1=Giuseppe |last2=Zimatore |first2=Giovanna |date=18 December 2017 |title=RQA correlations on real business cycles time series |journal=Indian Academy of Sciences – Conference Series |volume=1 |issue=1 |pages=35–41 |doi=10.29195/iascs.01.01.0009 |doi-access=free}}</ref> developed the so-called recurrence quantification correlation index (RQCI) to test correlations of RQA on a sample signal and then investigated the application to business time series. The said index has been proven to detect hidden changes in time series. Further, Orlando et al.,<ref>{{Cite journal |last1=Orlando |first1=Giuseppe |last2=Zimatore |first2=Giovanna |date=1 May 2018 |title=Recurrence quantification analysis of business cycles |url=https://www.sciencedirect.com/science/article/abs/pii/S0960077918300924 |journal=Chaos, Solitons & Fractals |language=en |volume=110 |pages=82–94 |bibcode=2018CSF...110...82O |doi=10.1016/j.chaos.2018.02.032 |issn=0960-0779 |s2cid=85526993|url-access=subscription }}</ref> over an extensive dataset, shown that recurrence quantification analysis may help in anticipating transitions from laminar (i.e. regular) to turbulent (i.e. chaotic) phases such as USA GDP in 1949, 1953, etc. Last but not least, it has been demonstrated that recurrence quantification analysis can detect differences between macroeconomic variables and highlight hidden features of economic dynamics.

=== Complexity and education ===
Focusing on issues of student persistence with their studies, Forsman, Moll and Linder explore the "viability of using complexity science as a frame to extend methodological applications for physics education research", finding that "framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics".<ref>{{Cite journal |last1=Forsman |first1=Jonas |last2=Moll |first2=Rachel |last3=Linder |first3=Cedric |date=2014 |title=Extending the theoretical framing for physics education research: An illustrative application of complexity science |journal=Physical Review Special Topics - Physics Education Research |volume=10 |issue=2 |pages=020122 |bibcode=2014PRPER..10b0122F |doi=10.1103/PhysRevSTPER.10.020122 |doi-access=free |hdl=10613/2583|hdl-access=free }}</ref>

=== Complexity in healthcare research and practice ===

Healthcare systems are prime examples of complex systems, characterized by interactions among diverse stakeholders, such as patients, providers, policymakers, and researchers, across various sectors like health, government, community, and education. These systems demonstrate properties like non-linearity, emergence, adaptation, and feedback loops.<ref name=":0">{{Cite journal |last1=Kitson |first1=Alison |last2=Brook |first2=Alan |last3=Harvey |first3=Gill |last4=Jordan |first4=Zoe |last5=Marshall |first5=Rhianon |last6=O’Shea |first6=Rebekah |last7=Wilson |first7=David |date=2018-03-01 |title=Using Complexity and Network Concepts to Inform Healthcare Knowledge Translation |url=https://www.ijhpm.com/article_3385.html |journal=International Journal of Health Policy and Management |language=en |volume=7 |issue=3 |pages=231–243 |doi=10.15171/ijhpm.2017.79 |issn=2322-5939 |pmc=5890068 |pmid=29524952}}</ref> Complexity science in healthcare frames [[knowledge translation]] as a dynamic and interconnected network of processes—problem identification, knowledge creation, synthesis, implementation, and evaluation—rather than a linear or cyclical sequence. Such approaches emphasize the importance of understanding and leveraging the interactions within and between these processes and stakeholders to optimize the creation and movement of knowledge. By acknowledging the complex, adaptive nature of healthcare systems, [[Complexity Science|complexity science]] advocates for continuous stakeholder engagement, [[transdisciplinary]] collaboration, and flexible strategies to effectively translate research into practice.<ref name=":0" />

=== Complexity and biology ===
Complexity science has been applied to living organisms, and in particular to biological systems. Within the emerging field of [[fractal physiology]], bodily signals, such as heart rate or brain activity, are characterized using [[entropy]] or fractal indices. The goal is often to assess the state and the health of the underlying system, and diagnose potential disorders and illnesses.{{citation needed|date=July 2024}}

===Complexity and chaos theory===
Complex systems theory is related to [[chaos theory]], which in turn has its origins more than a century ago in the work of the French mathematician [[Henri Poincaré]]. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order.<ref>Hayles, N. K. (1991). ''[https://books.google.com/books?id=9g9QDwAAQBAJ&pg=PR7 Chaos Bound: Orderly Disorder in Contemporary Literature and Science]''. Cornell University Press, Ithaca, NY.</ref> Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions of the system, though in practice this is impossible to do with arbitrary accuracy.

The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex.<ref name="PC98">[[Paul Cilliers|Cilliers, P.]] (1998). ''Complexity and Postmodernism: Understanding Complex Systems'', Routledge, London.</ref> This is referred to as the "[[edge of chaos]]".<ref>[[Per Bak]] (1996). ''How Nature Works: The Science of Self-Organized Criticality'', Copernicus, New York, U.S.</ref>

[[File:Lorenz attractor yb.svg|thumb|right|200px|A plot of the [[Lorenz attractor]]]]

When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as it is within chaos theory, in which it prevails. As stated by Colander,<ref>Colander, D. (2000). ''The Complexity Vision and the Teaching of Economics'', E. Elgar, Northampton, Massachusetts.</ref> the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.<ref name="PC98" /> For recent examples in economics and business see Stoop et al.<ref>{{Cite journal |last1=Stoop |first1=Ruedi |last2=Orlando |first2=Giuseppe |last3=Bufalo |first3=Michele |last4=Della Rossa |first4=Fabio |date=2022-11-18 |title=Exploiting deterministic features in apparently stochastic data |journal=Scientific Reports |language=en |volume=12 |issue=1 |pages=19843 |bibcode=2022NatSR..1219843S |doi=10.1038/s41598-022-23212-x |issn=2045-2322 |pmc=9674651 |pmid=36400910}}</ref> who discussed [[Android (operating system)|Android]]'s market position, Orlando<ref>{{Cite journal |last=Orlando |first=Giuseppe |date=2022-06-01 |title=Simulating heterogeneous corporate dynamics via the Rulkov map |url=https://www.sciencedirect.com/science/article/pii/S0954349X22000121 |journal=Structural Change and Economic Dynamics |language=en |volume=61 |pages=32–42 |doi=10.1016/j.strueco.2022.02.003 |issn=0954-349X|url-access=subscription }}</ref> who explained the corporate dynamics in terms of mutual synchronization and chaos regularization of bursts in a group of chaotically bursting cells and Orlando et al.<ref>{{Cite journal |last1=Orlando |first1=Giuseppe |last2=Bufalo |first2=Michele |last3=Stoop |first3=Ruedi |date=2022-02-01 |title=Financial markets' deterministic aspects modeled by a low-dimensional equation |journal=Scientific Reports |language=en |volume=12 |issue=1 |pages=1693 |bibcode=2022NatSR..12.1693O |doi=10.1038/s41598-022-05765-z |issn=2045-2322 |pmc=8807815 |pmid=35105929}}</ref> who modelled financial data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity) with a low-dimensional deterministic model.

Therefore, the main difference between chaotic systems and complex systems is their history.<ref>Buchanan, M. (2000). ''Ubiquity : Why catastrophes happen'', three river press, New-York.</ref> Chaotic systems do not rely on their history as complex ones do. Chaotic behavior pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'.{{clarify|date=September 2011}} On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist [[Murray Gell-Mann]] called "an accumulation of frozen accidents".<ref>Gell-Mann, M. (1995). What is Complexity?  Complexity 1/1, 16-19</ref> In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations.

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===Complexity and network science===
A complex system is usually composed of many components and their interactions. Such a system can be represented by a network where nodes represent the components and links represent their interactions.<ref name="DorogovtsevMendes2003">{{Cite book |last1=Dorogovtsev |first1=S.N. |title=Evolution of Networks |last2=Mendes |first2=J.F.F. |year=2003 |isbn=9780198515906 |volume=51 |pages=1079 |doi=10.1093/acprof:oso/9780198515906.001.0001 |arxiv=cond-mat/0106144}}</ref><ref name="Newman2010">{{Cite book |last=Newman |first=Mark |url=https://cds.cern.ch/record/1281254 |title=Networks |year=2010 |isbn=9780199206650 |doi=10.1093/acprof:oso/9780199206650.001.0001}}{{Dead link|date=July 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> For example, the [[Internet]] can be represented as a network composed of nodes (computers) and links (direct connections between computers). Other examples of complex networks include social networks, financial institution interdependencies,<ref>{{Cite journal |last1=Battiston |first1=Stefano |last2=Caldarelli |first2=Guido |last3=May |first3=Robert M. |last4=Roukny |first4=tarik |last5=Stiglitz |first5=Joseph E. |date=2016-09-06 |title=The price of complexity in financial networks |journal=Proceedings of the National Academy of Sciences |language=en |volume=113 |issue=36 |pages=10031–10036 |bibcode=2016PNAS..11310031B |doi=10.1073/pnas.1521573113 |pmc=5018742 |pmid=27555583 |doi-access=free}}</ref> airline networks,<ref name="BarratBarthelemy2004">{{Cite journal |last1=Barrat |first1=A. |last2=Barthelemy |first2=M. |last3=Pastor-Satorras |first3=R. |last4=Vespignani |first4=A. |year=2004 |title=The architecture of complex weighted networks |journal=Proceedings of the National Academy of Sciences |volume=101 |issue=11 |pages=3747–3752 |arxiv=cond-mat/0311416 |bibcode=2004PNAS..101.3747B |doi=10.1073/pnas.0400087101 |issn=0027-8424 |pmc=374315 |pmid=15007165 |doi-access=free}}</ref> and biological networks.