There is a tremendous literature on complex systems out there, but I'd especially like to alert users of Wiki to some software being developed at the Santa Fe Institute called Swarm. See www.santafe.edu 
. Ed Buffaloe
Check the new Swarm web site at www.swarm.org
See also Ceptual Institute, which is looking for friendly and constructive people, asking "Your comments are welcome", but has not yet a Wiki Forum, what they really deserve.
www.ceptualinstitute.com Orchestration of Multiple Stochastic Systems.
complex-systems.ucsd.edu is a lab in San Diego studying complex systems.
The science of complex systems was first made popular by the Santa Fe Institute (SFI). This group of complex systems theorists and practitioners offer the following definition:
"Complexity refers to the condition of the universe which is integrated and yet too rich and varied for us to understand in simple common ? ways. We can understand many parts of the universe in these ways, but the larger more intricately related phenomena can only be understood by principles and patterns-not in detail."
This concept is important to us because the nature business and IT systems are becoming more complex. For almost a century our manufacturing model was reasonably stable. Rules for productivity, market dominance, and company success were well understood. However, the Information Age has turned previous "knowns" on their head. Today, no one can predict what or how rapidly new technologies will be developed. No one can accurately predict how supply chains will be affected or how customers will respond. A good business plan is only a guess.
Even small-to-medium-sized business are not insulated from this effect. Satellite communications, the Internet, and air transports commonly provide ways of rapidly moving corporate resources from place to place. All of us are now connected through a global market of online customers and suppliers, supply chain partnerships, and international franchise competition. As Susan Kelly and Mary Allison [1] suggest, businesses that don't understand the nature of complex system thinking and take advantage of it "will be at the mercy of an increasing number of sudden and unexpected shifts in the marketplace. As uncertainty grows exponentially with today's high rate of technological change and the fallout from it, so does the pressure of global markets." Many executives try to respond to this with yesterday's mindset and linear cause-and-effect thinking. Often, these responses will intensify an already downward spiral. Despite well-conceived plans and well-intended actions, a company that operates without complex-systems thinking will find itself unable to respond to the ever-increasing complexity of the business world.
Primary Issues
Common to any discussion of complex systems are several fundamental ideas.
First and most basic among these is agents. In complex systems, these are the autonomous entities that interact to carry out their particular tasks.
Another fundamental concept is that these agents are adaptive. That is, the agents must be able to react to their environment and possibly change their behavior based on what is learned.
Complex systems are also characterized by emergence. Emergence is a coherent pattern that arises out of interactions among agents. For example, the process of an entire ant colony being fed was not programmed. It emerged from some very simple rule programmed into each ant. In other words, emergence is a by-product of individuals-not an choreographed result. Emergent results can be good as well as bad, and therefore must be considered when developing agent-based systems.
Successful emergent systems often exist between order and chaos. As for any organism or organization, being orderly or chaotic all the time would result in death. However, the area in between is necessary for continued existence and fitness.
Lastly, nature can teach us a lot about designing complex systems. It has been solving large combinatorial problems for billions of years. It makes sense, then, for us to consider notions such as parasitism, symbiosis, reproduction, genetics, mitosis, and survival-of-the fittest when developing our agent-based systems. For example, British Telecom is using the model of ants and pheromones in its call-routing network. Here, successful calls leave an equivalent of pheromones to guide future calls.
1) Kelly, Susanne, and Mary Ann Allison, The Complexity Advantage: How the Science of Complexity Can Help Your Business Achieve Peak Performance, McGraw-Hill, New York, 1999. ISBN:0070014000
See System Theory and Ludwig Von Bertalanffy.
See original on c2.com