Deranged persons can refer to individuals who display signs of mental instability and abnormal behavior. Some of the synonyms used to describe such individuals may include mentally ill, insane, lunatic, or psychotic. Each term essentially describes an individual who is not in a sound state of mind and may exhibit irrational or dangerous behavior. Other synonyms that are closely related to deranged persons include unhinged, disturbed, and unbalanced. While the use of these terms can vary depending on the context in which they are used, they all essentially convey the idea of an individual whose mental state is unstable and potentially dangerous.