Singular vs. Plural – Meaning of ‘Plural of Plural’ vs. ‘Singular of Plural’

"Dynamics" can be either singular or plural, depending on usage. http://i.word.com/idictionary/dynamics

• The science of Dynamics is singular. "Dynamics is important for Physics majors to study."
  "Group Dynamics is a useful managerial tool."

• a specific instance of "a pattern or process of change, growth or activity" can be called a dynamic. So in contrasting two or more of these you would use "dymamics" as plural. "Your family dynamic was different from mine." "Our family dynamics were different."

So I would say that your first example refers to the study of population dynamics, whereas the second refers to the varying dynamics of two or more populations.

There is/ are still a couple of months left until the end of semester

"Couple" is a number-transparent noun, meaning that the number of the whole noun phrase is determined not by the head of the NP, but by the number of the oblique (i.e. the complement of of).

Some number-transparent nouns can take singular and plural obliques (A lot of errors were made ~ "a lot of work was done").

But because "couple" means "two" or "a small number", it takes only plural obliques, so in your example, the correct verb is the plural "are".