verb (v)

• attach (oneself) to a person or thing in a neurotic way(verb.social)

  Example:
  He fixates on his mother, even at the age of 40.
  

  source: wordnet30
• pay attention to exclusively and obsessively(verb.perception)

  source: wordnet30
• make fixed, stable or stationary(verb.change)

  Synonym:
  fix
  

  source: wordnet30
• become fixed (on)(verb.change)

  Example:
  Her eyes fixated on a point on the horizon.
  

  Synonym:
  settle on
  

  source: wordnet30