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.