Disconnecting any part of the system will produce drastic changes in the systems behavior. I tend to see these characteristics of the system as another way of describing what we call linearity. This seems logical to me because I have spent a great deal of time working with chaos theory and nonlinear dynamics, i.e. I try to explain phenomena using terms and ideas that I am familiar with, as does everyone else. This is why the new field of complexity theory has so many different definitions and descriptions for its nomenclature. The thermodynamicist sees entropy as a measure of complexity, the topologist sees fractal dimension and scaling as a measure of complexity, a computer science expert correlates information content as a measure of complexity, and so on.
Additional complexity appears whenever one description bifurcates from another.
He also claims that the level of complexity depends on how close you look at the system. If most of us look at a stone lying in the street we see a very simple system with a small number ways for us to interact with it. We can throw it, kick it, etc. But if a geologist looks at the same system he sees a much greater number of possible interactions. So the system gets more complex as we look closer at it.