Perturb vs. Disturb

Disturb is to distract, disrupt, etc. Perturb is to disturb and subsequently cause annoyance. Like when someone disturbs your slept, you are then perturbed.

Disturbed is usually used as a transitive verb, used when something acts on another, e.g. he disturbed me. Perturbed is an intransitive adverb describing an agitated state without associating it with an direct external cause, e.g. "When I came upon him, he seemed perturbed".

English needs such separate words because it generally doe not contain transitive and intransitive versions of the same verbs as Japanese does.

As of late, however, disturbed has begun to take on the meaning of an intransitive adverb with one of two meanings: 1, the same usage as perturbed (which is still rare enough to be called incorrect as of yet), and 2, insane or otherwise not in full command of one's faculties.

There is no such thing as a transitive or intransitive adverb. Both "perturbed" and "disturbed" are participle adjectives when they follow the verb "to be" or other stative verbs i.e. seem, feel, sound, etc. Both perturbed and disturbed are passive verbs using past participle forms when the "by" agent is used. For example, "She was disturbed by the story". In an active sentence, the verb immediately converts to the present participle adjective form, as in "The story was disturbing to her". I hope this helps!

In the scientific sense, if you perturb a system, like an ecosystem, say, you poke it or mess with it in a very controlled and usually small way to see what happens to it. However, if you disturb a system, the implication is that the system is pretty much wrecked: the system no longer displays the behavior that it displayed in its nondisturbed state.
For example, if you introduce a non-native specie into an ecosystem, if you want to say that it integrated itself into that ecosystem with relative little harm done, you might say that the change "perturbed" the system. However, if you want to emphasize the destructiveness of the nonnative specie, you might say that its introduction disturbed the ecosystem.