Complex Systems could be described as models or physical systems that exhibit a surprising sensitivity to either their controlling input parameters or to some non-linear combinational effect of the parameters. Most of the physical systems we encounter are non-linear and although we like to try to understand them in terms of linear behaving components, we are increasingly often having to turn to complex systems analysis methods.
Some systems are described as Complex and Adaptive - often systems that involve some inherent life or even intelligence. We are still exploring the full implications of "life" and "intelligence" in very simple models.
Research in this area looks at just how simple a system can be while still exhibiting behaviour inexplicable in terms of linear analysis. It is interesting to try to characterise systems in terms of their complexity. Our understanding of just what complexity actually is continues to develop. A useful set of ideas is related to the algorithmic information content (AIC) - or the information needed to unambiguously specify or describe a system. Ideas from computational complexity and indeed quantum computational complexity are playing important roles in this field. A closely related area is understanding emergence in systems, since emergent phenomena seem to particularly abound in complex and adaptive systems.
Understanding complexity impinges on some fairly deep philosophical ideas and consequently there is plenty of controversy about it. One can however make some pragmatic inroads into comparing different systems with some ad hoc metrics. Some useful books at a relatively accessible level are:
Our work in this area is centred around pragmatic ways to assign information content metrics or entropy functions. This involves considering the context for describing a system configuration - what is its state compared to the possible and probable states it might have in its context. Of particular interest is understanding the complexity of graph structures and other spatial arrangements found in systems such as artificial life models and network models.
As well as investigating quantifiable metrics and statistical properties, there are also various applications of complex networks such as: road traffic simulations; human traffic and building evacuation models; and overlay networks that arise from computational grids of services.