Note that While this doesn't serve as a intented answer, this is intended to help the others to solve it if there is a way with pure math. Because I'm unable to provide a solution using purely mathematical methods. I can propose a programming-based solution, but I'm uncertain about its validity according to OP.
The upper bound is
One sheep takes 2 units of time to be caught, while the other sheep moves in the opposite direction towards to the wolf to increase the distance between them, after the wolf catches the first, then it will take an additional 4 units of time. I won't go into the details as it is easily understandable.
Of course there is an assumption to find the upper bound:
The second caught sheep will not be caught while passing through the wolf and the wolf ignores the second sheep while the wolf is after the first,
If we go back to the original question;
At all times,
the primary wolf pursues the sheep that is closest to it. If a wolf chooses to chase one sheep, it should maintain its direction until the second sheep becomes closer than the one it is currently pursuing.
the sheep should consider this fact as well.
as a graphical representation;
please note that
The movements of the wolf are represented by blue, the first sheep is indicated by green, and the second sheep's movements are shown in orange.
this shows how the first sheep is caught:
When the wolf approaches, both sheep begin to move away. If the wolf pursues one sheep, that sheep will attempt to create as much distance as possible from the other sheep. Meanwhile, the second sheep ensures that it maintains a distance from the wolf that is always greater than or equal to the distance between the wolf and the first sheep. As a result, such a graph should be formed.
After the first sheep is caught, the rest is
a straight line between the second sheep and the wolf and should be easily calculated.