Complex system

Complex system

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A complex system is a system
System
System is a set of interacting or interdependent components forming an integrated whole....

 composed of interconnected parts that as a whole exhibit one or more properties (behavior among the possible properties) not obvious from the properties of the individual parts.

A system’s complexity
Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

 may be of one of two forms: disorganized complexity and organized complexity. In essence, disorganized complexity is a matter of a very large number of parts, and organized complexity is a matter of the subject system (quite possibly with only a limited number of parts) exhibiting emergent
Emergence
In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....

 properties.

Examples of complex system
System
System is a set of interacting or interdependent components forming an integrated whole....

s for which complexity models have been developed include ant colonies
Ant colony
An ant colony is an underground lair where ants live, eat and mate. Colonies consist of a series of underground chambers, connected to each other and the surface of the earth by small tunnels. There are rooms for nurseries, food storage, and mating...

, human economies
Complexity economics
Complexity economics is the application of complexity science to the problems of economics. It studies computer simulations to gain insight into economic dynamics, and avoids the assumption that the economy is a system in equilibrium.- Models :...

 and social structures
Sociology and complexity science
Sociology and complexity science is the term used to describe a growing network of research taking place at the intersection of sociology and complexity science....

, climate
Climate
Climate encompasses the statistics of temperature, humidity, atmospheric pressure, wind, rainfall, atmospheric particle count and other meteorological elemental measurements in a given region over long periods...

, nervous system
Nervous system
The nervous system is an organ system containing a network of specialized cells called neurons that coordinate the actions of an animal and transmit signals between different parts of its body. In most animals the nervous system consists of two parts, central and peripheral. The central nervous...

s, cells
Cell (biology)
The cell is the basic structural and functional unit of all known living organisms. It is the smallest unit of life that is classified as a living thing, and is often called the building block of life. The Alberts text discusses how the "cellular building blocks" move to shape developing embryos....

 and living things, including human beings, as well as modern energy or telecommunication
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...

 infrastructures. Indeed, many systems of interest to humans are complex systems.

Complex systems are studied by many areas of natural science
Natural science
The natural sciences are branches of science that seek to elucidate the rules that govern the natural world by using empirical and scientific methods...

, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, and social science. Fields that specialize in the interdisciplinary study of complex systems include systems theory
Systems theory
Systems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...

, complexity theory, systems ecology
Systems ecology
Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem...

, and cybernetics
Cybernetics
Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...

.

Overview


A complex system is a network of heterogeneous components that interact nonlinearly, to give rise to emergent behavior. The term complex systems has multiple meanings depending on its scope:
  • A specific kind of system
    System
    System is a set of interacting or interdependent components forming an integrated whole....

    s which are complex
    Complexity
    In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

  • A field of science
    Science
    Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

     studying these systems; see further complex systems
    Complex systems
    Complex systems present problems in mathematical modelling.The equations from which complex system models are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of systems of nature that are considered...

  • A paradigm
    Paradigm
    The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...

     that complex systems have to be studied with non-linear dynamics; see further complexity
    Complexity
    In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...



Various informal descriptions of complex systems have been put forward, and these may give some insight into their properties. A special edition of Science
Science (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....

about complex systems highlighted several of these:
  • A complex system is a highly structured system, which shows structure with variations (N. Goldenfeld and Kadanoff
    Leo Kadanoff
    Leo Philip Kadanoff is an American physicist. He is a professor of physics at the University of Chicago and a former President of the American Physical Society . He has contributed to the fields of statistical physics, chaos theory, and theoretical condensed matter physics.-Biography:Kadanoff...

    )
  • A complex system is one whose evolution is very sensitive to initial conditions or to small perturbations, one in which the number of independent interacting components is large, or one in which there are multiple pathways by which the system can evolve (Whitesides
    George M. Whitesides
    George M. Whitesides is an American chemist and professor of chemistry at Harvard University. He is best known for his work in the areas of NMR spectroscopy, organometallic chemistry, molecular self-assembly, soft lithography, microfabrication, microfluidics, and nanotechnology...

     and Ismagilov)
  • A complex system is one that by design or function or both is difficult to understand and verify (Weng, Bhalla and Iyengar)
  • A complex system is one in which there are multiple interactions between many different components (D. Rind)
  • Complex systems are systems in process that constantly evolve and unfold over time (W. Brian Arthur
    W. Brian Arthur
    William Brian Arthur is an economist credited with influencing and describing the modern theory of increasing returns. He has lived and worked in Northern California for many years. He is an authority on economics in relation to complexity theory, technology and financial markets...

    ).

History


Although one can argue that humans have been studying complex systems for thousands of years, the modern scientific study of complex systems is relatively young when compared to conventional science areas with simple system assumption such as physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

. The history of the scientific study of these systems follows several different research trends.

In the area of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, arguably the largest contribution to the study of complex systems was the discovery of chaos
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

 in deterministic systems, a feature of certain dynamical systems that is strongly related to nonlinearity
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

. The study of neural networks
Neural Networks
Neural Networks is the official journal of the three oldest societies dedicated to research in neural networks: International Neural Network Society, European Neural Network Society and Japanese Neural Network Society, published by Elsevier...

 was also integral in advancing the mathematics needed to study complex systems.

The notion of self-organizing systems is tied up to work in nonequilibrium thermodynamics, including that pioneered by chemist
Chemist
A chemist is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties such as density and acidity. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms...

 and Nobel laureate Ilya Prigogine
Ilya Prigogine
Ilya, Viscount Prigogine was a Russian-born naturalized Belgian physical chemist and Nobel Laureate noted for his work on dissipative structures, complex systems, and irreversibility.-Biography :...

 in his study of dissipative structures.

Chaotic systems


For a dynamical system to be classified as chaotic
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

, it must have the following properties:
  1. it must be sensitive to initial conditions,
  2. it must be topologically mixing, and
  3. its periodic orbits must be dense
    Dense set
    In topology and related areas of mathematics, a subset A of a topological space X is called dense if any point x in X belongs to A or is a limit point of A...

    .


Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior.

Complex adaptive systems


Complex adaptive system
Complex adaptive system
Complex adaptive systems are special cases of complex systems. They are complex in that they are dynamic networks of interactions and relationships not aggregations of static entities...

s (CAS) are special cases of complex systems. They are complex
Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

 in that they are diverse and made up of multiple interconnected elements and adaptive in that they have the capacity to change and learn from experience. Examples of complex adaptive systems include the stock market
Stock market
A stock market or equity market is a public entity for the trading of company stock and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.The size of the world stock market was estimated at about $36.6 trillion...

, social insect and ant
Ant
Ants are social insects of the family Formicidae and, along with the related wasps and bees, belong to the order Hymenoptera. Ants evolved from wasp-like ancestors in the mid-Cretaceous period between 110 and 130 million years ago and diversified after the rise of flowering plants. More than...

 colonies, the biosphere
Biosphere
The biosphere is the global sum of all ecosystems. It can also be called the zone of life on Earth, a closed and self-regulating system...

 and the ecosystem
Ecosystem
An ecosystem is a biological environment consisting of all the organisms living in a particular area, as well as all the nonliving , physical components of the environment with which the organisms interact, such as air, soil, water and sunlight....

, the brain
Human brain
The human brain has the same general structure as the brains of other mammals, but is over three times larger than the brain of a typical mammal with an equivalent body size. Estimates for the number of neurons in the human brain range from 80 to 120 billion...

 and the immune system
Immune system
An immune system is a system of biological structures and processes within an organism that protects against disease by identifying and killing pathogens and tumor cells. It detects a wide variety of agents, from viruses to parasitic worms, and needs to distinguish them from the organism's own...

, the cell
Cell (biology)
The cell is the basic structural and functional unit of all known living organisms. It is the smallest unit of life that is classified as a living thing, and is often called the building block of life. The Alberts text discusses how the "cellular building blocks" move to shape developing embryos....

 and the developing embryo
Embryo
An embryo is a multicellular diploid eukaryote in its earliest stage of development, from the time of first cell division until birth, hatching, or germination...

, manufacturing business
Manufacturing
Manufacturing is the use of machines, tools and labor to produce goods for use or sale. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale...

es and any human social group-based endeavor in a cultural and social system such as political parties
Political party
A political party is a political organization that typically seeks to influence government policy, usually by nominating their own candidates and trying to seat them in political office. Parties participate in electoral campaigns, educational outreach or protest actions...

 or communities
Community
The term community has two distinct meanings:*a group of interacting people, possibly living in close proximity, and often refers to a group that shares some common values, and is attributed with social cohesion within a shared geographical location, generally in social units larger than a household...

. This includes some large-scale online systems, such as collaborative tagging or social bookmarking
Social bookmarking
Social bookmarking is a method for Internet users to organize, store, manage and search for bookmarks of resources online. Unlike file sharing, the resources themselves aren't shared, merely bookmarks that reference them....

 systems.

Nonlinear system


The behavior of nonlinear systems is not subject to the principle of superposition
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...

 while that of Linear systems is subject to superposition. Thus, a nonlinear system
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

 is one whose behavior can't be expressed as a sum of the behaviors of its parts (or of their multiples).

Features of complex systems


Complex systems may have the following features:

Cascading Failures
Due to the strong coupling between components in complex systems, a failure in one or more components can lead to cascading failures which may have catastrophic consequences on the functioning of the system.


Difficult to determine boundaries
It can be difficult to determine the boundaries of a complex system. The decision is ultimately made by the observer.


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
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

: but despite this flux, there may be pattern stability, see synergetics
Synergetics
Synergetics is an interdisciplinary science explaining the formation and self-organization of patterns and structures in open systems far from thermodynamic equilibrium. It is founded by Hermann Haken, inspired by the laser theory....

.


Complex systems may have a memory
The history of a complex system may be important. Because complex systems are dynamical systems they change over time, and prior states may have an influence on present states. More formally, complex systems often exhibit hysteresis
Hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

.


Complex systems may be nested
The components of a complex system may themselves be complex systems. For example, an economy
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 is made up of organisations, which are made up of people
Person
A person is a human being, or an entity that has certain capacities or attributes strongly associated with being human , for example in a particular moral or legal context...

, which are made up of cell
Cell (biology)
The cell is the basic structural and functional unit of all known living organisms. It is the smallest unit of life that is classified as a living thing, and is often called the building block of life. The Alberts text discusses how the "cellular building blocks" move to shape developing embryos....

s - all of which are complex systems.


Dynamic network of multiplicity
As well as coupling rules, the dynamic network of a complex system is important. Small-world
Small-world network
In mathematics, physics and sociology, a small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps...

 or scale-free
Scale-free network
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P of nodes in the network having k connections to other nodes goes for large values of k as...

 networks 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
Cerebral cortex
The cerebral cortex is a sheet of neural tissue that is outermost to the cerebrum of the mammalian brain. It plays a key role in memory, attention, perceptual awareness, thought, language, and consciousness. It is constituted of up to six horizontal layers, each of which has a different...

 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
Emergence
In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....

, 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, the termites in a mound have physiology, biochemistry and biological development that are at one level of analysis, but their social behavior
Social behavior
In physics, physiology and sociology, social behavior is behavior directed towards society, or taking place between, members of the same species. Behavior such as predation which involves members of different species is not social...

 and mound building is a property that emerges from the collection of termites and needs to be analysed at a different level.


Relationships are non-linear
In practical terms, this means a small perturbation may cause a large effect (see butterfly effect
Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state...

), a proportional effect, or even no effect at all. In linear systems, effect is always directly proportional to cause. See nonlinearity
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

.


Relationships contain feedback loops
Both negative (damping) and positive (amplifying) feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

 are always found in complex systems. The effects of an element's behaviour are fed back to in such a way that the element itself is altered.

See also


  • Agent-based model
  • Biological organisation
  • Complex (disambiguation)
  • Complexity (disambiguation)
    Complexity (disambiguation)
    In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement.Complexity may also refer to:* Complex systems* Complexity theory * Kolmogorov complexity...

  • Complex adaptive system
    Complex adaptive system
    Complex adaptive systems are special cases of complex systems. They are complex in that they are dynamic networks of interactions and relationships not aggregations of static entities...

  • Complex network
    Complex network
    In the context of network theory, a complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in real graphs...

  • Dissipative system
    Dissipative system
    A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter....

  • Fractals
  • Innovation butterfly
    Innovation butterfly
    The Innovation Butterfly is a metaphor that describes how seemingly minor perturbations to project plans in a system connecting markets, demand, product features, and a firm's capabilities can steer the project, or an entire portfolio of projects, down an irreversible path in terms of technology...

  • Mixed Reality
    Mixed reality
    Mixed reality refers to the merging of real and virtual worlds to produce new environments and visualisations where physical and digital objects co-exist and interact in real time...

  • System equivalence
    System equivalence
    In the systems sciences the term system equivalence is the notion that a parameter or component of a system behaves in a similar way as a parameter or component of a different system. Similarity means that mathematically the parameters/components will be indistinguishable from each other...

  • Systems theory
    Systems theory
    Systems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...


Further reading



  • Ignazio Licata & Ammar Sakaji (eds) (2008). Physics of Emergence and Organization, ISBN 13 978-981-277-994-6, World Scientific
    World Scientific
    World Scientific Publishing is a publisher of scientific, technical, and medical books and journals. The company was founded in 1981 and now employs more than 200 staff at its headquarters in Singapore, with offices worldwide in New Jersey, California, London, New Delhi, Tianjin, Sydney, Hong...

     and Imperial College Press
    Imperial College Press
    Imperial College Press was formed in 1995 and is a partnership between Imperial College of Science, Technology and Medicine in London and World Scientific publishing....

    .



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