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Thus, a complex nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts (or of their multiples).
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nonlinearly
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Complex systems may be open
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27 Mar 12
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[edit] Complex adaptive systems
Complex adaptive systems (CAS) are special cases of complex systems. They are complex 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, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the developing embryo, manufacturing businesses and any human social group-based endeavor in a cultural and social system such as political parties or communities. This includes some large-scale online systems, such as collaborative tagging or social bookmarking systems.
[edit] Nonlinear system
The behavior of nonlinear systems is not subject to the principle of superposition while that of Linear systems is subject to superposition. Thus, a nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts (or of their multiples).
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12 Feb 12
carlos puentesA complex system is a system 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.
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10 Feb 12
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05 Aug 11
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29 Jun 11
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03 Nov 10
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system’s complexity may be of one of two forms: disorganized complexity and organized complexity
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disorganized complexity is a matter of a very large number of parts
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organized complexity is a matter of the subject system (quite possibly with only a limited number of parts) exhibiting emergent properties
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Examples of complex systems
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ant colonies, human economies and social structures, climate, nervous systems, cells and living things, including human beings, as well as modern energy or telecommunication infrastructures
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complex system is a network of heterogeneous components that interact nonlinearly, to give rise to emergent behavior
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highly structured system, which shows structure with variations
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complex system is
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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
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one that by design or function or both is difficult to understand and verify
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one in which there are multiple interactions between many different components
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systems in process that constantly evolve and unfold over time
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feature of certain dynamical systems that is strongly related to nonlinearity
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area of mathematics
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largest contribution to the study of complex systems was the discovery of chaos in deterministic systems
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study of neural networks
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also integral in advancing the mathematics needed to study complex systems
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Types of complex systems
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Chaotic systems
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For a dynamical system to be classified as chaotic
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it must be sensitive to initial conditions
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it must be topologically mixing
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its periodic orbits must be dense
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each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories
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arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior
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Complex adaptive systems
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Complex adaptive systems (CAS) are special cases of complex systems
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they have the capacity to change and learn from experience
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stock market
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brain and the immune system
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social insect and ant colonies
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manufacturing businesses
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any human social group-based endeavor in a cultural and social system such as political parties or communities
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some large-scale online systems, such as collaborative tagging or social bookmarking systems
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Nonlinear system
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a nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts (or of their multiples)
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07 Oct 10
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14 Mar 10
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07 Mar 10
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A complex system is one in which there are multiple interactions between many different components (D. Rind)
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Complex systems are systems in process that constantly evolve and unfold over time (
W. Brian Arthur -
Complex systems may exhibit behaviors that are emergent, which is to say that while the results may be deterministic, 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 and mound building is a property that emerges from the collection of termites and needs to be analysed at a different level.
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Science Vol. 284. No. 5411 (1999)]
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Boundaries are difficult to determine
It can be difficult to determine the boundaries of a complex system. The decision is ultimately made by the observer.
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complex systems specifically consist of a large number of mutually interacting dynamical parts.
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Relationships contain feedback loops
Both negative (damping) and positive (amplifying) feedback are often 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.
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Dynamic network of multiplicity
As well as coupling rules, the dynamic network of a complex system is important. Small-world or scale-free 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 for example, we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions.
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Complex systems are open
Complex systems in nature are usually open systems — that is, they exist in a thermodynamic gradient and dissipate energy. In other words, complex systems are usually far from energetic equilibrium: but despite this flux, there may be pattern stability. See synergetics.
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Complex systems 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.
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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.
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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, effect is always directly proportional to cause. See nonlinearity.
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29 May 06
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26 Jun 05
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14 May 05
Nick GallGreat overview of complex systems.
via_delicious_20101217 ImportedFurl20071006 pinboardimport20141106 Complexity
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A complex system is a system whose properties are not fully explained by an understanding of its component parts. Complex systems consist of a large number of mutually interacting and interwoven parts, entities or agents. They are woven out of many parts, the Latin complexus comes from the Greek pleko or plektos, meaning "to plait or twine." (Gell-Mann). Complex systems is also often used as a broad term addressing a research approach which includes ideas and techniques from chaos theory, artificial life, evolutionary computation and genetic algorithms.
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26 Mar 05
Triple Entendreopen nested history short-range non-linear feedback loops emergence boundaries
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