Generally speaking, any mathematical model that is time dependent will be considered a 'dynamic' system, some engineering descriptions will say dynamic systems are described as systems having the ability to store and release energy.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
As far as nonlinear things go. Most real world systems are nonlinear. However, it's difficult to say immediately whether something is, before one goes on to model it.
But to give an example from the modelling of a tentacle:
Biological real world systems get complicated fast, and end up being inherently, nonlinear.
However we often linearize such systems around a operating point (Taylor Series for example) once we have a clear understanding of what it may be. Will will drastically reduce your problem with a given amount of (hopefully) small error.