A linear system can be decomposed into subsystems. Such decomposition fails however in the case of nonlinear systems. When the behaviors of the constituents of a system are highly coherent and correlated, the system cannot be treated even approximately as a collection of uncoupled individual parts. Instead, some particular global or nonlocal description is required, taking into account that individual constituents cannot be fully characterized without reference to larger scale structures of the system such as order parameters. (Chemero & Silberstein, 2008, p. 16).But, why does decomposition fail in the case of nonlinear systems? Think of a double pendulum. Why can that not be decomposed into two pendulums?
It is not a part of mechanistic explanation that one treat systems as "a collection of uncoupled individual parts" if in fact they are a collection nonlinearly coupled parts. Rather, I would think that mechanistic explanations of systems of nonlinearly coupled components should involve treating them as systems of nonlinearly coupled components. I know that it is common to think that nonlinearity causes explanatory problems, but it can't be that nonlinearity forces us to treat such systems as collections of uncoupled individual parts.
Moreover, in either the linear or the nonlinear cases, the MDC approach (and I think the Bechtel approach) to mechanistic explanation invokes higher level descriptions (global descriptions) which would be the things to be explained by the lower level mechanisms. So, there is no "instead" about particular global or nonlocal descriptions.
Nor, need the mechanist "fully characterize" the individual constituents without reference to larger structure of the system. Isn't that what "fully characterize" means one does? Refer to the larger structure?
To repeat, however, I think there could be something problematic about nonlinear systems, but I don't see that C&S have put their finger on it.