How do constraints affect the behaviour of a complex system?

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In a system consisting of simple agents, how do constraints affect the emergent macroscopic behaviours? In nature, there are many examples of emergent behaviour in complex systems, for example, the Gutenberg-Richter law of earthquakes, the power-law behaviour of price fluctuations, the connectivity of social networks etc. However, these complex systems are finite in size. How does the finiteness of these systems perturb the inherent (ideal) behaviour that one would observe in an infinite system? Can one extract the scaling behaviour of the perturbation from finite systems that would eventually allow one to extrapolate to the infinite system? The notion of finite-size scaling in critical systems is one such example, but in a limited domain. Another related question is whether smaller systems are inherently more predictable due to the constraints. If yes, can one exploit this increased predictability to extrapolate the predictability of larger systems? These investigations are first pursued in simplified complex systems. TheResearch Area: Complexity ScienceResearch Area: Complexity ScienceStrategic Area: Mathematical Sciences & Physical Sciences