Perseveration is a fixation on something or someone. Autistic people frequently spend hours of time studying an unusual topic of interest (such as airplanes, dogs, or books by J. K. Rowling). Other people may notice that they spend a long time disappearing into books or websites about the interest, or find that the autistic person loves to share information about it, sometimes to the point that it becomes annoying.
Perseveration can have a positive impact on an autistic person's life. They can harness their intense focus and specialized knowledge to become experts in a particular field. For example, an autistic girl whose special interest is computer science could go on to have a very successful career at Silicon Valley. People who perserverate show remarkable focus and ability to study for extended periods of time.
Perserveration is not always positive. For example, if a woman becomes frustrated while building a robot, and begins thinking It's not working, it's not working, it's not working... then this is not good. Her anxiety is taking over her thoughts and preventing her to do what she wants to do.
When perserverating turns negative, it is best to break the cycle. Autistic people can get a drink, take a walk, or take a bathroom break, and then come back.
Some semanting overlapping with fixation, mania, otaku, hobby, collecting.