The times that the joggers (4:00 a.m. to 10:00 a.m.) and police officers (8:00 p.m. to 4:00 a.m.) coincides with the availability of certain Pokemon, such as Hoothoot at night (8:00 p.m. to 4:00 a.m.).
So as you can (hopefully) see, joggers and police officers only battle in those times listed above.
Joggers - 4:00 AM - 10:00 AM
Officers - 8:00 PM - 4:00 AM
There are no other timed battles like that, but there are battles that you can have with trainers in different places during different days of the week.
Here is a Link to those trainers and locations.