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If you do a search (Google, Wikipedia, etc) you will find "dynamic
equilibrium" usefully defined
only for chemical and biological interactions. In Mechanics a
somewhat related set of useful concepts is stable vs unstable
equilibrium.
Note that in mechanics we say that an object at rest under the action
of a set of forces which sum to zero is in a state of static
equilibrium. This same object could be said to be in a state of
dynamic equilibrium when viewed from a different frame, in which the
object is in motion. This distinction does not add much and AFAICT is
not used.