Sometimes the usage is arbitrary, but there are two main tendencies in use: is the writer referring to the scientific field concerned with forces, or are they referring to those forces directly? Are they a scientific speaker, where the choice really matters, or are they a casual speaker?
Dynamics (or Dynamics) takes a singular verb when it refers to the subject of study. Compare to physics or (in some dialects) maths. For example:
Dynamics is also the scientific study of the forces that produce movement.
Informally, dynamics is the study of forces and motion. More formally, dynamics is the branch of mechanics that deals with the effect that forces have on the motion of objects.
However, when one is referring to forces directly, without concern for a wider body of study, then dynamics takes a plural noun and refers to multiple forces acting simultaneously. The Collins Dictionary specifies this usage in both British and American English. The American entry is as follows:
dynamics ... noun [with pl. v. for 2a & b]
- the branch of mechanics dealing with the motions of material bodies under the action of given forces; kinetics
the various forces, physical, oral, economic, etc., operating in any field
the way such forces shift or change in relation to one another
the study of such forces
- the effect of varying degrees of loudness or softness in the performance of music
So this would hold true for the discussion of forces in a non-physics context, like in biology:
Active site dynamics are quenched within holo BLVRB.
This is the general usage I'd expect in non-scientific contexts too. Your average speaker will tend not to think of "dynamics" as a singular entity. Specific searches of the Corpus of Contemporary American English supports this: "the dynamics is" has 28 hits, and "the dynamics are" has 105 hits, and "dynamics are" is in general more common.
That said, this line can seem fuzzy; I have seen dynamics used in cases where it could refer to multiple forces or to the study of forces:
On this single landscape, dynamics is driven by gradient of the potential landscape, which is closely related to the steady- state probability distribution of the enlarged dimensions, and the probability flux, which has a curl nature.
Technical language is fun. At this point, it's up to authors or editors to determine what they mean and apply verbs accordingly.
A final nota bene: Collins claims that UK and American speakers differ in whether the musical term dynamics is treated as singular or plural. In the UK entry, it is treated as singular; in the American entry, it is treated as plural. Frankly I've seen both forms used online interchangeably, so I don't know how reliable that distinction is.