static (behavior), model
The dynamics of a system describe the changes of the system's variables over time.
For many purposes it is sufficient to consider which steady states a system has and how it behaves at (static) or near those states (linearization).
For a non-linear system, linearization is an approximation by a linear description for a specific equilibrium point. It is valid for local dynamics around that point, but can not represent the global dynamics of the original system, nor local dynamics around other equilibrium points (except special cases). Linear approximations are used because they are simpler and easier to handle than non-linear systems. Two special theories of linear approximations are BST and MCT, discussed in the historical review in Section 1.1.
Local dynamic behavior (local dynamics) is the behavior of a system within a small area around an equilibrium point. Within that area, the linear approximation of the original system is good enough to give a valid representation of the original system.
Global dynamic behavior (global dynamics) is the behavior of a system over the full range of values in its domain.