Complex Systems(complexity, wiki, imported, Proteus)
There are many definitions of
complexity, therefore many natural, artificial and abstract objects or networks can be considered to be
complex systems, and their study (
complexity science) is highly interdisciplinary. Examples of complex
systems include
ant-hills,
ants themselves,
human economies,
nervous systems,
cells and living things, including human beings, as well as modern energy or telecommunication infrastructures.
Beyond the fact that these things are all (wiktionary:network|networks) of some kind, and that they are complex, it may appear that they have little in common, hence that the term "complex system" is vacuous. However, all complex systems are held to have behavioural and structural features in common, which at least to some degree unites them as phenomena. They are also united theoretically, because all these systems may, in principle, be
modelled with varying degrees of success by a certain kind of mathematics. It is therefore possible to state clearly what it is that these systems are supposed to have in common with each other, in relatively formal terms.
Definition
The term
complex system has no precise definition but can often be taken to mean a system with many strongly-coupled
degrees of freedom. Traditional methods of mathematical modeling are adept at handling systems with few degrees of freedom that interact strongly, such as the paradigmatic
simple harmonic oscillator, while statistical methods are useful for systems with very many degrees of freedom all of which interact weakly, such as a
box of gas. Complex systems such as the
Potts model occupy the intermediary regime, where local and global phenomena interact in complicated, often
nonlinear ways. (For consistency, the examples cited above are all drawn from physics even though complex systems are studied by many scientific disciplines.)
Applications of complex systems theory
The study of complex systems is bringing new vitality to many areas of science where a more typical
reductionist strategy has fallen short.
Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines including
neuroscience,
meteorology,
chemistry,
physics,
computer science,
psychology,
artificial life,
evolutionary computation,
economics,
earthquake prediction,
heart cell synchronisation,
immune systems,
reaction-diffusion systems,
molecular biology,
epilepsy and inquiries into the nature of living cells themselves. In these endeavours, scientists often seek simple non-linear coupling rules which
lead to complex phenomena (rather than describe - see above), but this need not be the case. Human societies (and probably human
brains) are complex systems in which neither the components nor the couplings are simple. Nevertheless, they exhibit many of the hallmarks of complex systems.
Traditionally, engineering has striven to keep its systems linear, because that makes them simpler to build and to predict. However, many physical systems (for example
lasers) are inherently "complex systems" in terms of the definition above, and engineering practice must now include elements of complex systems research.
Information theory applies well to the complex adaptive systems, CAS, through the concepts of object oriented design.
Features of complex systems in nature
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.
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.
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.
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.
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.
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.
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.
May produce emergent phenomena
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.
Quotes
- From Sync by Steven Strogatz: "Every decade or so, a grandiose theory comes along, bearing similar aspirations and often brandishing an ominous-sounding C-name. In the 1960 it was cybernetics. In the '70s it was catastrophe theory. Then came chaos theory in the '80s and complexity theory in the '90s."
Various informal descriptions of
complex systems have been put forward, and these may give some insight into their properties. A special edition of
Science about
complex systems
Science Vol. 284. No. 5411 (1999).
highlighted several of these:
- A complex system is a highly structured system, which shows structure with variations (Goldenfeld and 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 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).
See also
External links
Institutes
Directories
Articles
Mailing Lists, Discussion Groups and Forums
Specialized Wikis and Sites about Complex Systems
Conferences
Komplexes System
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Some content adapted from the Wikinfo article "Complex system" under the GNU Free Documentation License.
(last updated by Proteus, 7:27pm EDT - Tue, Apr 03 2007)
