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Complex system

February 16, 2024

"Complex systems" redirects here. For the journal, see Complex Systems (journal).

A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe.[citation needed]

Complex systems are systems whose behavior is intrinsically difficult to model due to the dependencies, competitions, relationships, or other types of interactions between their parts or between a given system and its environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links to their interactions.

The term complex systems often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment.[1] The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to reductionism, which attempts to explain systems in terms of their constituent parts and the individual interactions between them.

As an interdisciplinary domain, complex systems draws contributions from many different fields, such as the study of self-organization and critical phenomena from physics, that of spontaneous order from the social sciences, chaos from mathematics, adaptation from biology, and many others. Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology, economics, psychology, and biology.

Key concepts edit

 
Gosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life[2]

Adaptation edit

Complex adaptive systems are special cases of complex systems that are adaptive in that they have the capacity to change and learn from experience. Examples of complex adaptive systems include the stock market, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the developing embryo, cities, manufacturing businesses and any human social group-based endeavor in a cultural and social system such as political parties or communities.[3]

Features edit

Complex systems may have the following features:[4]

Complex systems may be open
Complex systems are usually open systems — that is, they exist in a thermodynamic gradient and dissipate energy. In other words, complex systems are frequently far from energetic equilibrium: but despite this flux, there may be pattern stability,[5] see synergetics.
Complex systems may exhibit critical transitions
 
Graphical representation of alternative stable states and the direction of critical slowing down prior to a critical transition (taken from Lever et al. 2020).[6] Top panels (a) indicate stability landscapes at different conditions. Middle panels (b) indicate the rates of change akin to the slope of the stability landscapes, and bottom panels (c) indicate a recovery from a perturbation towards the system's future state (c.I) and in another direction (c.II).
Critical transitions are abrupt shifts in the state of ecosystems, the climate, financial systems or other complex systems that may occur when changing conditions pass a critical or bifurcation point.[7][8][9][10] The 'direction of critical slowing down' in a system's state space may be indicative of a system's future state after such transitions when delayed negative feedbacks leading to oscillatory or other complex dynamics are weak.[6]
Complex systems may be nested
The components of a complex system may themselves be complex systems. For example, an economy is made up of organisations, which are made up of people, which are made up of cells – all of which are complex systems. The arrangement of interactions within complex bipartite networks may be nested as well. More specifically, bipartite ecological and organisational networks of mutually beneficial interactions were found to have a nested structure.[11][12] This structure promotes indirect facilitation and a system's capacity to persist under increasingly harsh circumstances as well as the potential for large-scale systemic regime shifts.[13][14]
Dynamic network of multiplicity
As well as coupling rules, the dynamic network of a complex system is important. Small-world or scale-free networks[15][16] which have many local interactions and a smaller number of inter-area connections are often employed. Natural complex systems often exhibit such topologies. In the human cortex for example, we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions.
May produce emergent phenomena
Complex systems may exhibit behaviors that are emergent, which is to say that while the results may be sufficiently determined by the activity of the systems' basic constituents, they may have properties that can only be studied at a higher level. For example, empirical food webs display regular, scale-invariant features across aquatic and terrestrial ecosystems when studied at the level of clustered 'trophic' species.[17][18] Another example is offered by the termites in a mound which have physiology, biochemistry and biological development at one level of analysis, whereas their social behavior and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level.
Relationships are non-linear
In practical terms, this means a small perturbation may cause a large effect (see butterfly effect), a proportional effect, or even no effect at all. In linear systems, the effect is always directly proportional to cause. See nonlinearity.
Relationships contain feedback loops
Both negative (damping) and positive (amplifying) feedback are always found in complex systems. The effects of an element's behavior are fed back in such a way that the element itself is altered.

History edit

In 1948, Dr. Warren Weaver published an essay on "Science and Complexity",[19] exploring the diversity of problem types by contrasting problems of simplicity, disorganized complexity, and organized complexity. Weaver's described these as "problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole."

While the explicit study of complex systems dates at least to the 1970s,[20] the first research institute focused on complex systems, the Santa Fe Institute, was founded in 1984.[21][22] Early Santa Fe Institute participants included physics Nobel laureates Murray Gell-Mann and Philip Anderson, economics Nobel laureate Kenneth Arrow, and Manhattan Project scientists George Cowan and Herb Anderson.[23] Today, there are over 50 institutes and research centers focusing on complex systems.[citation needed]

Since the late 1990s, the interest of mathematical physicists in researching economic phenomena has been on the rise. The proliferation of cross-disciplinary research with the application of solutions originated from the physics epistemology has entailed a gradual paradigm shift in the theoretical articulations and methodological approaches in economics, primarily in financial economics. The development has resulted in the emergence of a new branch of discipline, namely "econophysics," which is broadly defined as a cross-discipline that applies statistical physics methodologies which are mostly based on the complex systems theory and the chaos theory for economics analysis.[24]

The 2021 Nobel Prize in Physics was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their work to understand complex systems. Their work was used to create more accurate computer models of the effect of global warming on the Earth's climate.[25]

Applications edit

Complexity in practice edit

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 edit

Jane Jacobs described cities as being a problem in organized complexity in 1961, citing Dr. Weaver's 1948 essay.[26] 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.[27]

Complexity economics edit

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.[28] 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.,[29] 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 edit

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".[30]

Complexity and biology edit

Complexity science has been applied to living organisms, and in particular to biological systems. One of the areas of research is the emergence and evolution of intelligent systems. Analyses of the parameters of intellectual systems, patterns of their emergence and evolution, distinctive features, and the constants and limits of their structures and functions made it possible to measure and compare the capacity of communications (~100 to 300 million m/s), to quantify the number of components in intellectual systems (~1011 neurons), and to calculate the number of successful links responsible for cooperation (~1014 synapses)[31] 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.

Complexity and chaos theory edit

Complex systems theory is rooted in 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.[32] 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. Ilya Prigogine argued[33] that complexity is non-deterministic and gives no way whatsoever to precisely predict the future.[34]

The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex.[35] This is referred to as the "edge of chaos".[36]

 
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,[37] 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.[35] For recent examples in economics and business see Stoop et al.[38] who discussed Android's market position, Orlando [39] 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.[40] 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.[41] 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'.[clarification needed] 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".[42] 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.

Complexity and network science edit

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.[43][44] 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,[45] airline networks,[46] and biological networks.

Notable scholars edit

See also edit

References edit

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Further reading edit

  • .
  • L.A.N. Amaral and J.M. Ottino, Complex networks — augmenting the framework for the study of complex system, 2004.
  • Chu, D.; Strand, R.; Fjelland, R. (2003). "Theories of complexity". Complexity. 8 (3): 19–30. Bibcode:2003Cmplx...8c..19C. doi:10.1002/cplx.10059.
  • Walter Clemens, Jr., , SUNY Press, 2013.
  • Gell-Mann, Murray (1995). "Let's Call It Plectics". Complexity. 1 (5): 3–5. Bibcode:1996Cmplx...1e...3G. doi:10.1002/cplx.6130010502.
  • A. Gogolin, A. Nersesyan and A. Tsvelik, , Cambridge University Press, 1999.
  • Nigel Goldenfeld and Leo P. Kadanoff, Simple Lessons from Complexity, 1999
  • Kelly, K. (1995). Out of Control, Perseus Books Group.
  • Orlando, Giuseppe Orlando; Pisarchick, Alexander; Stoop, Ruedi (2021). Nonlinearities in Economics. Dynamic Modeling and Econometrics in Economics and Finance. Vol. 29. doi:10.1007/978-3-030-70982-2. ISBN 978-3-030-70981-5. S2CID 239756912.
  • Syed M. Mehmud (2011),
  • Donald Snooks, Graeme (2008). "A general theory of complex living systems: Exploring the demand side of dynamics". Complexity. 13 (6): 12–20. Bibcode:2008Cmplx..13f..12S. doi:10.1002/cplx.20225.
  • Stefan Thurner, Peter Klimek, Rudolf Hanel: Introduction to the Theory of Complex Systems, Oxford University Press, 2018, ISBN 978-0198821939
  • (2014).

External links edit

 
Wikimedia Commons has media related to Complex systems.
 
Look up complex systems in Wiktionary, the free dictionary.
  • "The Open Agent-Based Modeling Consortium".
  • . Archived from the original on 2017-12-05. Retrieved 2017-09-22.
  • "Santa Fe Institute".
  • "The Center for the Study of Complex Systems, Univ. of Michigan Ann Arbor".
  • "INDECS". (Interdisciplinary Description of Complex Systems)
  • . Archived from the original on 2018-08-30. Retrieved 2018-08-29.
  • Jessie Henshaw (October 24, 2013). "Complex Systems". Encyclopedia of Earth.
  • Complex systems in scholarpedia.
  • Complex Systems Society
  • based on Luis M. Rocha, 1999.

February 16, 2024
complex, system, redirects, here, journal, complex, systems, journal, complex, system, system, composed, many, components, which, interact, with, each, other, examples, complex, systems, earth, global, climate, organisms, human, brain, infrastructure, such, po. Complex systems redirects here For the journal see Complex Systems journal A complex system is a system composed of many components which may interact with each other Examples of complex systems are Earth s global climate organisms the human brain infrastructure such as power grid transportation or communication systems complex software and electronic systems social and economic organizations like cities an ecosystem a living cell and ultimately the entire universe citation needed Complex systems are systems whose behavior is intrinsically difficult to model due to the dependencies competitions relationships or other types of interactions between their parts or between a given system and its environment Systems that are complex have distinct properties that arise from these relationships such as nonlinearity emergence spontaneous order adaptation and feedback loops among others Because such systems appear in a wide variety of fields the commonalities among them have become the topic of their independent area of research In many cases it is useful to represent such a system as a network where the nodes represent the components and links to their interactions The term complex systems often refers to the study of complex systems which is an approach to science that investigates how relationships between a system s parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment 1 The study of complex systems regards collective or system wide behaviors as the fundamental object of study for this reason complex systems can be understood as an alternative paradigm to reductionism which attempts to explain systems in terms of their constituent parts and the individual interactions between them As an interdisciplinary domain complex systems draws contributions from many different fields such as the study of self organization and critical phenomena from physics that of spontaneous order from the social sciences chaos from mathematics adaptation from biology and many others Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines including statistical physics information theory nonlinear dynamics anthropology computer science meteorology sociology economics psychology and biology Contents 1 Key concepts 1 1 Adaptation 2 Features 3 History 4 Applications 4 1 Complexity in practice 4 2 Complexity of cities 4 3 Complexity economics 4 4 Complexity and education 4 5 Complexity and biology 4 6 Complexity and chaos theory 4 7 Complexity and network science 5 Notable scholars 6 See also 7 References 8 Further reading 9 External linksKey concepts edit nbsp Gosper s Glider Gun creating gliders in the cellular automaton Conway s Game of Life 2 Adaptation edit Complex adaptive systems are special cases of complex systems that are adaptive in that they have the capacity to change and learn from experience Examples of complex adaptive systems include the stock market social insect and ant colonies the biosphere and the ecosystem the brain and the immune system the cell and the developing embryo cities manufacturing businesses and any human social group based endeavor in a cultural and social system such as political parties or communities 3 Features editComplex systems may have the following features 4 Complex systems may be open Complex systems are usually open systems that is they exist in a thermodynamic gradient and dissipate energy In other words complex systems are frequently far from energetic equilibrium but despite this flux there may be pattern stability 5 see synergetics Complex systems may exhibit critical transitions nbsp Graphical representation of alternative stable states and the direction of critical slowing down prior to a critical transition taken from Lever et al 2020 6 Top panels a indicate stability landscapes at different conditions Middle panels b indicate the rates of change akin to the slope of the stability landscapes and bottom panels c indicate a recovery from a perturbation towards the system s future state c I and in another direction c II Critical transitions are abrupt shifts in the state of ecosystems the climate financial systems or other complex systems that may occur when changing conditions pass a critical or bifurcation point 7 8 9 10 The direction of critical slowing down in a system s state space may be indicative of a system s future state after such transitions when delayed negative feedbacks leading to oscillatory or other complex dynamics are weak 6 Complex systems may be nested The components of a complex system may themselves be complex systems For example an economy is made up of organisations which are made up of people which are made up of cells all of which are complex systems The arrangement of interactions within complex bipartite networks may be nested as well More specifically bipartite ecological and organisational networks of mutually beneficial interactions were found to have a nested structure 11 12 This structure promotes indirect facilitation and a system s capacity to persist under increasingly harsh circumstances as well as the potential for large scale systemic regime shifts 13 14 Dynamic network of multiplicity As well as coupling rules the dynamic network of a complex system is important Small world or scale free networks 15 16 which have many local interactions and a smaller number of inter area connections are often employed Natural complex systems often exhibit such topologies In the human cortex for example we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions May produce emergent phenomena Complex systems may exhibit behaviors that are emergent which is to say that while the results may be sufficiently determined by the activity of the systems basic constituents they may have properties that can only be studied at a higher level For example empirical food webs display regular scale invariant features across aquatic and terrestrial ecosystems when studied at the level of clustered trophic species 17 18 Another example is offered by the termites in a mound which have physiology biochemistry and biological development at one level of analysis whereas their social behavior and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level Relationships are non linear In practical terms this means a small perturbation may cause a large effect see butterfly effect a proportional effect or even no effect at all In linear systems the effect is always directly proportional to cause See nonlinearity Relationships contain feedback loops Both negative damping and positive amplifying feedback are always found in complex systems The effects of an element s behavior are fed back in such a way that the element itself is altered History editIn 1948 Dr Warren Weaver published an essay on Science and Complexity 19 exploring the diversity of problem types by contrasting problems of simplicity disorganized complexity and organized complexity Weaver s described these as problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole While the explicit study of complex systems dates at least to the 1970s 20 the first research institute focused on complex systems the Santa Fe Institute was founded in 1984 21 22 Early Santa Fe Institute participants included physics Nobel laureates Murray Gell Mann and Philip Anderson economics Nobel laureate Kenneth Arrow and Manhattan Project scientists George Cowan and Herb Anderson 23 Today there are over 50 institutes and research centers focusing on complex systems citation needed Since the late 1990s the interest of mathematical physicists in researching economic phenomena has been on the rise The proliferation of cross disciplinary research with the application of solutions originated from the physics epistemology has entailed a gradual paradigm shift in the theoretical articulations and methodological approaches in economics primarily in financial economics The development has resulted in the emergence of a new branch of discipline namely econophysics which is broadly defined as a cross discipline that applies statistical physics methodologies which are mostly based on the complex systems theory and the chaos theory for economics analysis 24 The 2021 Nobel Prize in Physics was awarded to Syukuro Manabe Klaus Hasselmann and Giorgio Parisi for their work to understand complex systems Their work was used to create more accurate computer models of the effect of global warming on the Earth s climate 25 Applications editComplexity in practice edit 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 edit Jane Jacobs described cities as being a problem in organized complexity in 1961 citing Dr Weaver s 1948 essay 26 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 27 Complexity economics edit 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 28 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 29 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 edit 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 30 Complexity and biology edit Complexity science has been applied to living organisms and in particular to biological systems One of the areas of research is the emergence and evolution of intelligent systems Analyses of the parameters of intellectual systems patterns of their emergence and evolution distinctive features and the constants and limits of their structures and functions made it possible to measure and compare the capacity of communications 100 to 300 million m s to quantify the number of components in intellectual systems 1011 neurons and to calculate the number of successful links responsible for cooperation 1014 synapses 31 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 Complexity and chaos theory edit Complex systems theory is rooted in chaos theory which in turn has its origins more than a century ago in the work of the French mathematician Henri Poincare Chaos is sometimes viewed as extremely complicated information rather than as an absence of order 32 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 Ilya Prigogine argued 33 that complexity is non deterministic and gives no way whatsoever to precisely predict the future 34 The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex 35 This is referred to as the edge of chaos 36 nbsp A plot of the Lorenz attractorWhen 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 37 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 35 For recent examples in economics and business see Stoop et al 38 who discussed Android s market position Orlando 39 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 40 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 41 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 clarification needed 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 42 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 Complexity and network science edit 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 43 44 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 45 airline networks 46 and biological networks Notable scholars editRobert McCormick Adams Christopher Alexander Philip Anderson Kenneth Arrow Robert Axelrod W Brian Arthur Per Bak Bela H Banathy Albert Laszlo Barabasi Gregory Bateson Ludwig von Bertalanffy Alexander Bogdanov Samuel Bowles Guido Caldarelli Paul Cilliers Walter Clemens Jr James P Crutchfield Chris Danforth Peter Sheridan Dodds Brian Enquist Joshua Epstein Doyne Farmer Jay Forrester Nigel R Franks Murray Gell Mann Nigel Goldenfeld Vittorio Guidano James Hartle F A Hayek John Holland Alfred Hubler Arthur Iberall Johannes Jaeger Stuart Kauffman J A Scott Kelso David Krakauer Simon A Levin Ellen Levy Robert May Donella Meadows Jose Fernando Mendes Melanie Mitchell Cris Moore Edgar Morin Harold Morowitz Scott Page Luciano Pietronero David Pines Vladimir Pokrovskii William T Powers Ilya Prigogine Sidney Redner Jerry Sabloff Cosma Shalizi Herbert Simon Dave Snowden Sergei Starostin Steven Strogatz Stefan Thurner Alessandro Vespignani Andreas Wagner Duncan Watts Geoffrey West Stephen Wolfram David Wolpert Steen Rasmussen Yaneer Bar YamSee also edit nbsp Systems science portalBiological organisation Chaos theory Cognitive modeling Cognitive Science Complex disambiguation Complex adaptive system Complex networks Complexity Complexity disambiguation Complexity economics Complexity Science Hub Vienna Cybernetics Decision engineering Dissipative system Dual phase evolution Dynamical system Dynamical systems theory Emergence Enterprise systems engineering Fractal Fractal physiology Generative sciences Hierarchy theory Homeokinetics Interdependent networks Invisible hand Mixed reality Multi agent system Network science Neuroscience and intelligence fr Noogenese Nonlinearity Pattern oriented modeling Percolation Percolation theory Process architecture Self organization Sociology and complexity science System accident System dynamics System equivalence Systems Engineering Systems theory Systems theory in anthropology Tektology Ultra large scale systems Volatility uncertainty complexity and ambiguityReferences edit Bar Yam Yaneer 2002 General Features of Complex Systems PDF Encyclopedia of Life Support Systems Archived PDF from the original on 2022 10 09 Retrieved 16 September 2014 Daniel Dennett 1995 Darwin s Dangerous Idea Penguin Books London ISBN 978 0 14 016734 4 ISBN 0 14 016734 X Skrimizea Eirini Haniotou Helene Parra Constanza 2019 On the complexity turn in planning An adaptive rationale to navigate spaces and times of uncertainty Planning Theory 18 122 142 doi 10 1177 1473095218780515 S2CID 149578797 Alan Randall 2011 Risk and Precaution Cambridge University Press ISBN 9781139494793 Pokrovskii Vladimir 2021 Thermodynamics of Complex Systems Principles and applications IOP Publishing Bristol UK Bibcode 2020tcsp book P a b Lever J Jelle Leemput Ingrid A Weinans Els Quax Rick Dakos Vasilis Nes Egbert H Bascompte Jordi Scheffer Marten 2020 Foreseeing the future of mutualistic communities beyond collapse Ecology Letters 23 1 2 15 doi 10 1111 ele 13401 PMC 6916369 PMID 31707763 Scheffer Marten Carpenter Steve Foley Jonathan A Folke Carl Walker Brian October 2001 Catastrophic shifts in ecosystems Nature 413 6856 591 596 Bibcode 2001Natur 413 591S doi 10 1038 35098000 ISSN 1476 4687 PMID 11595939 S2CID 8001853 Scheffer Marten 26 July 2009 Critical transitions in nature and society Princeton University Press ISBN 978 0691122045 Scheffer Marten Bascompte Jordi Brock William A Brovkin Victor Carpenter Stephen R Dakos Vasilis Held Hermann van Nes Egbert H Rietkerk Max Sugihara George September 2009 Early warning signals for critical transitions Nature 461 7260 53 59 Bibcode 2009Natur 461 53S doi 10 1038 nature08227 ISSN 1476 4687 PMID 19727193 S2CID 4001553 Scheffer Marten Carpenter Stephen R Lenton Timothy M Bascompte Jordi Brock William Dakos Vasilis Koppel Johan van de Leemput Ingrid A van de Levin Simon A Nes Egbert H van Pascual Mercedes Vandermeer John 19 October 2012 Anticipating Critical Transitions Science 338 6105 344 348 Bibcode 2012Sci 338 344S doi 10 1126 science 1225244 hdl 11370 92048055 b183 4f26 9aea e98caa7473ce ISSN 0036 8075 PMID 23087241 S2CID 4005516 Archived from the original on 24 June 2020 Retrieved 10 June 2020 Bascompte J Jordano P Melian C J Olesen J M 24 July 2003 The nested assembly of plant animal mutualistic networks Proceedings of the National Academy of Sciences 100 16 9383 9387 Bibcode 2003PNAS 100 9383B doi 10 1073 pnas 1633576100 PMC 170927 PMID 12881488 Saavedra Serguei Reed Tsochas Felix Uzzi Brian January 2009 A simple model of bipartite cooperation for ecological and organizational networks Nature 457 7228 463 466 Bibcode 2009Natur 457 463S doi 10 1038 nature07532 ISSN 1476 4687 PMID 19052545 S2CID 769167 Bastolla Ugo Fortuna Miguel A Pascual Garcia Alberto Ferrera Antonio Luque Bartolo Bascompte Jordi April 2009 The architecture of mutualistic networks minimizes competition and increases biodiversity Nature 458 7241 1018 1020 Bibcode 2009Natur 458 1018B doi 10 1038 nature07950 ISSN 1476 4687 PMID 19396144 S2CID 4395634 Lever J Jelle Nes Egbert H van Scheffer Marten Bascompte Jordi 2014 The sudden collapse of pollinator communities Ecology Letters 17 3 350 359 doi 10 1111 ele 12236 hdl 10261 91808 ISSN 1461 0248 PMID 24386999 A L Barab asi R Albert 2002 Statistical mechanics of complex networks Reviews of Modern Physics 74 1 47 94 arXiv cond mat 0106096 Bibcode 2002RvMP 74 47A CiteSeerX 10 1 1 242 4753 doi 10 1103 RevModPhys 74 47 S2CID 60545 M Newman 2010 Networks An Introduction Oxford University Press ISBN 978 0 19 920665 0 Cohen J E Briand F Newman C M 1990 Community Food Webs Data and Theory Berlin Heidelberg New York Springer p 308 doi 10 1007 978 3 642 83784 5 ISBN 9783642837869 Briand F Cohen J E 1984 Community food webs have scale invariant structure Nature 307 5948 264 267 Bibcode 1984Natur 307 264B doi 10 1038 307264a0 S2CID 4319708 Warren Weaver Oct 1948 Science and Complexity American Scientist 36 4 536 544 Retrieved 28 October 2023 Vemuri V 1978 Modeling of Complex Systems An Introduction New York Academic Press ISBN 978 0127165509 Ledford H 2015 How to solve the world s biggest problems Nature 525 7569 308 311 Bibcode 2015Natur 525 308L doi 10 1038 525308a PMID 26381968 History Santa Fe Institute Archived from the original on 2019 04 03 Retrieved 2018 05 17 Waldrop M M 1993 Complexity The emerging science at the edge of order and chaos Simon and Schuster Ho Y J Ruiz Estrada M A Yap S F 2016 The evolution of complex systems theory and the advancement of econophysics methods in the study of stock market crashes Labuan Bulletin of International Business amp Finance 14 68 83 Nobel in physics Climate science breakthroughs earn prize BBC News 5 October 2021 Jacobs Jane 1961 The Death and Life of Great American Cities New York Vintage Books pp 428 448 Cities scaling amp sustainability Santa Fe Institute Retrieved 28 October 2023 Orlando Giuseppe Zimatore Giovanna 18 December 2017 RQA correlations on real business cycles time series Indian Academy of Sciences Conference Series 1 1 35 41 doi 10 29195 iascs 01 01 0009 Orlando Giuseppe Zimatore Giovanna 1 May 2018 Recurrence quantification analysis of business cycles Chaos Solitons amp Fractals 110 82 94 Bibcode 2018CSF 110 82O doi 10 1016 j chaos 2018 02 032 ISSN 0960 0779 S2CID 85526993 Forsman Jonas Moll Rachel Linder Cedric 2014 Extending the theoretical framing for physics education research An illustrative application of complexity science Physical Review Special Topics Physics Education Research 10 2 020122 Bibcode 2014PRPER 10b0122F doi 10 1103 PhysRevSTPER 10 020122 hdl 10613 2583 Eryomin A L 2022 Biophysics of Evolution of Intellectual Systems Biophysics 67 2 320 326 Hayles N K 1991 Chaos Bound Orderly Disorder in Contemporary Literature and Science Cornell University Press Ithaca NY Prigogine I 1997 The End of Certainty The Free Press New York See also D Carfi 2008 Superpositions in Prigogine approach to irreversibility AAPP Physical Mathematical and Natural Sciences 86 1 1 13 a b Cilliers P 1998 Complexity and Postmodernism Understanding Complex Systems Routledge London Per Bak 1996 How Nature Works The Science of Self Organized Criticality Copernicus New York U S Colander D 2000 The Complexity Vision and the Teaching of Economics E Elgar Northampton Massachusetts Stoop Ruedi Orlando Giuseppe Bufalo Michele Della Rossa Fabio 2022 11 18 Exploiting deterministic features in apparently stochastic data Scientific Reports 12 1 19843 Bibcode 2022NatSR 1219843S doi 10 1038 s41598 022 23212 x ISSN 2045 2322 PMC 9674651 PMID 36400910 Orlando Giuseppe 2022 06 01 Simulating heterogeneous corporate dynamics via the Rulkov map Structural Change and Economic Dynamics 61 32 42 doi 10 1016 j strueco 2022 02 003 ISSN 0954 349X Orlando Giuseppe Bufalo Michele Stoop Ruedi 2022 02 01 Financial markets deterministic aspects modeled by a low dimensional equation Scientific Reports 12 1 1693 Bibcode 2022NatSR 12 1693O doi 10 1038 s41598 022 05765 z ISSN 2045 2322 PMC 8807815 PMID 35105929 Buchanan M 2000 Ubiquity Why catastrophes happen three river press New York Gell Mann M 1995 What is Complexity Complexity 1 1 16 19 Dorogovtsev S N Mendes J F F 2003 Evolution of Networks Vol 51 p 1079 arXiv cond mat 0106144 doi 10 1093 acprof oso 9780198515906 001 0001 ISBN 9780198515906 Newman Mark 2010 Networks doi 10 1093 acprof oso 9780199206650 001 0001 ISBN 9780199206650 permanent dead link Battiston Stefano Caldarelli Guido May Robert M Roukny tarik Stiglitz Joseph E 2016 09 06 The price of complexity in financial networks Proceedings of the National Academy of Sciences 113 36 10031 10036 Bibcode 2016PNAS 11310031B doi 10 1073 pnas 1521573113 PMC 5018742 PMID 27555583 Barrat A Barthelemy M Pastor Satorras R Vespignani A 2004 The architecture of complex weighted networks Proceedings of the National Academy of Sciences 101 11 3747 3752 arXiv cond mat 0311416 Bibcode 2004PNAS 101 3747B doi 10 1073 pnas 0400087101 ISSN 0027 8424 PMC 374315 PMID 15007165 Further reading editComplexity Explained L A N Amaral and J M Ottino Complex networks augmenting the framework for the study of complex system 2004 Chu D Strand R Fjelland R 2003 Theories of complexity Complexity 8 3 19 30 Bibcode 2003Cmplx 8c 19C doi 10 1002 cplx 10059 Walter Clemens Jr Complexity Science and World Affairs SUNY Press 2013 Gell Mann Murray 1995 Let s Call It Plectics Complexity 1 5 3 5 Bibcode 1996Cmplx 1e 3G doi 10 1002 cplx 6130010502 A Gogolin A Nersesyan and A Tsvelik Theory of strongly correlated systems Cambridge University Press 1999 Nigel Goldenfeld and Leo P Kadanoff Simple Lessons from Complexity 1999 Kelly K 1995 Out of Control Perseus Books Group Orlando Giuseppe Orlando Pisarchick Alexander Stoop Ruedi 2021 Nonlinearities in Economics Dynamic Modeling and Econometrics in Economics and Finance Vol 29 doi 10 1007 978 3 030 70982 2 ISBN 978 3 030 70981 5 S2CID 239756912 Syed M Mehmud 2011 A Healthcare Exchange Complexity Model Preiser Kapeller Johannes Calculating Byzantium Social Network Analysis and Complexity Sciences as tools for the exploration of medieval social dynamics August 2010 Donald Snooks Graeme 2008 A general theory of complex living systems Exploring the demand side of dynamics Complexity 13 6 12 20 Bibcode 2008Cmplx 13f 12S doi 10 1002 cplx 20225 Stefan Thurner Peter Klimek Rudolf Hanel Introduction to the Theory of Complex Systems Oxford University Press 2018 ISBN 978 0198821939 SFI 30 Foundations amp Frontiers 2014 External links edit nbsp Wikimedia Commons has media related to Complex systems nbsp Look up complex systems in Wiktionary the free dictionary The Open Agent Based Modeling Consortium Complexity Science Focus Archived from the original on 2017 12 05 Retrieved 2017 09 22 Santa Fe Institute The Center for the Study of Complex Systems Univ of Michigan Ann Arbor INDECS Interdisciplinary Description of Complex Systems Introduction to Complexity Free online course by Melanie Mitchell Archived from the original on 2018 08 30 Retrieved 2018 08 29 Jessie Henshaw October 24 2013 Complex Systems Encyclopedia of Earth Complex systems in scholarpedia Complex Systems Society Australian Complex systems research network Complex Systems Modeling based on Luis M Rocha 1999 CRM Complex systems research group The Center for Complex Systems Research Univ of Illinois at Urbana Champaign Retrieved from https en wikipedia org w index php title Complex system amp oldid 1201726435, wikipedia, wiki, book, books, library,

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