Complex Systems

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, 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 networks of some kind and 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 modeled 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.

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.

Applications 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, such as lasers, are inherently “complex systems” in terms of the definition above, and engineering practice must now include elements of complex systems research.

In practical terms, this means a small perturbation may cause a large “butterfly” effect, a proportional effect, or even no effect at all. In linear systems, effect is always directly proportional to cause. 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 in Nature exist in a thermodynamic gradient and dissipate energy. In other words, complex systems are usually far from energetic equilibrium. 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 analyzed 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.”
• 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).

External Links

• Supplements to the Proceedings of the National Academy of Sciences (PNAS):
• Adaptive Agents, Intelligence, and Emergent Human Organization: Capturing Complexity through Agent-Based Modeling
• Self-organized complexity in the physical, biological, and social sciences
• CSCS's Definition of Complex Systems
• NICO's About Complex Systems
• Complex networks - augmenting the framework for the study of complex system (Amaral & Ottino, 2004)
• Self-Organizing and Self-Replicating Paths to Autonomous Intelligence (A.I.)
• A New Kind of Science by Stephen Wolfram
• Plectics article from by Murray Gell-Mann
• Emergent Nature
• Simple Lessons from Complexity (May not be available)
• VisualComplexity.com - A visual exploration on mapping complex networks
• Modelling Complex Socio-Technical Systems using Morphological Analysis From the Swedish Morphological Society
• Theory of strongly correlated systems
• Complexity; a science at 30
• Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth