I define a complex system as a system that behaves differently from any model we can make of that system.
A complex system is characterised by non-linearities, by feedback from one part of the system to another and properties that emerge from its behaviour over time. These behaviours cannot be explained or derived from examining the subcomponents of the system.
The scientific approach - reductionism and simplification - will create models that do not explain the complex nature of a system or phenomenon.
The real meaning of the butterfy effect: In any model of a complex system, any deviation from reality whether it be in concept, relationship or data values will introduce errors such that the behaviour of the model will rapidly diverge from that of reality. The butterfy does not cause the tornado, omitting its influence (or that of any other butterfly) renders useless the predictive capability of the model. Similarly, it is not that the model behavuiour is critically dependent on initial conditions, it is critically dependent on every aspect of the model, including the affect of external perturbations.
Bernard Robertson-Dunn 2014