The Libyans knew when, and where, to find Doc Brown in 1985, because the Doc's past self told them.

https://www.reddit.com/r/FanTheories/comments/659u0j/back_to_the_future_the_libyans_knew_when_and/

In Back to the Future, when Doc Brown steals the plutonium needed for his time machine, only to be pursued by Libyan nationalists, he says: "Oh my god. They found me; I don't know how but they found me. RUN FOR IT, MARTY!!"

My theory is simple, but short: The Libyans knew when, and where, to find Doc Brown, because his past self had told them so. This solves the question / plot hole of how the Libyans were able to find the Doc in 1985.

Let me explain. In the film, Marty, before he returns to 1985, leaves a note /letter explaining everything to the past Doc Brown in 955. This, notably, as we see later in the film, results in future Doc knowing about the Libyans' arrival, as well as prompting him to wear a bulletproof vest. This, ultimately, saves his life.

However, I believe that's not all. I think that the past Doc Brown, in order to make sure the timeline was as preserved as possible, was also the same person to tip off the Libyans when he stole the plutonium from them. According to some, Doc Brown was the one to help the Libyans obtain the plutonium to begin with.

Likewise, this would also fit with the perspective of the past Doc Brown in 1955 in the film.

When Marty explains everything to him, the Doc wants him to remain at his house and not do, or interfere, with anything to preserve the timeline, and prevent anything from changing. (To prevent "the butterfly effect", if you will.) Unfortunately, Marty had already changed things by that point.

However, given how adamant and insistent the Doc is on "not changing anything", it stands to reason, too, that he would have to make sure the events leading up to the success of the time machine remained unaltered (or happened the same way) as well. This would include making sure that the Libyans found him, which would eventually result in Marty travelling back to 1955 in the DeLorean, and meeting his past self.

Or, in other words, the Doc was trying to stabilize (or form a more stable) timeline / time loop, even in spite of Marty's changes to the timeline.