My quick introduction
This is my personal view of complex systems, and thus, it could be incorrect, subjective and/or biased. But nevertheless, I'll try to do my best.
What is Complex System?
First and foremost we have to define what complex system is, that is, what we mean by that expression. This is necessary because otherwise we do not know clearly and unambiguously what is the subject we are talking about. There are multiple definitions of complexity, some of which are collected in the links section below. But the truth is that it is very hard to define rigorously and concisely what a complex system is and approaches currently used are to define necessary features some system has to have in order to be treated as a complex.
For what is it useful?
As always, the first question for anything we try to develop, use and/or understand is For what is it useful? and this question is hugely important since if we are doing something that has no application or use whatsoever, we are actually wasting precious time. So let's clarify why studding complex systems is useful.
Even though there is a disagreement about the question what is complex system there is no disagreement that complex systems are around us. Furthermore, there is no disagreement about certain systems being complex, like power grid, or human brain, etc. So it's obvious, at least for those certainly complex systems, that studying them is very useful and applicable. Now, even though there could be disagreements about certain system being complex or not, there is certainly no disagreement in the statement that there are multitude of complex systems in the real world.
What are the problems we are facing?
What tools and methods do we have to study it?
Mathematical tools, i.e. differential equations, are used in certain cases. But there are two problems with this approach. The first one is that it becomes intractable when approaching certain sizes. The second is that not all complex systems can be described in such way. Take for example power grid. It's behavior can not be described by differential equations.
The primary tool is simulation.
What do we want to achieve
There are multitude of things that we want to achieve, some of them being:
- make complex systems manageable.
- know how to use complexity to make better, more robust, systems.
Introductory, overview & tutorial papers
John Guckenheimer, Julio M. Ottino; Foundations for Complex Systems Research in the Physical Sciences and Engineering, Report from an NSF Workshop; September 2008. (local)
Shalizi, Cosma Rohilla; Methods and Techniques of Complex Systems Science: An Overview, Complex Systems Science in Biomedicine, Springer US, 2006, pp 33-114.(local)
Complexity Pages A
non-technical introduction to the new science of Chaos and
Bibliography "The Evolution of Complexity"
Society for Chaos Theory in Psychology & Life Sciences
Santa Fe Institute
Definitions of complexity
Evidences of complexity
Here and then I stumble on some description that is obviously describing situation in which interplay between different components produces some new (often erroneous :)) behavior. This is, IMHO, emergent behavior that is a key characteristic of complex systems. In this subsection I'll collect links to such cases.
The article which describes emergent insecurity from combining two components. The insecurity occurs only when the components are connected together in a certain, erroneous, way.
This blog entry describes a case in which two plugins (IcedTea and Moonlight) would crash browser when used together, but not when used separately. Furthermore, they would crash a browser under some specific circumstances.