The difference at its root is related to a distinction between active voice (corresponding to the present participle) versus passive voice (corresponding to the past participle).
In your example sentence, it can be said that "local times originate from X" (active voice) whereas "local times are perpetuated by Y" (passive voice). Note that latter can be written in active voice as "Y perpetuates local times". And the former can't be sensibly written in passive voice (originate, in the sense used here, is intransitive and agent-less).
The wikipedia article on paticiples explains this difference like so:
Participles may correspond to the active voice (active participles),
where the modified noun is taken to represent the agent of the action
denoted by the verb; or to the passive voice (passive participles),
where the modified noun represents the patient (undergoer) of that
action. Participles in particular languages are also often associated
with certain verbal aspects or tenses. The two types of participle in
English are traditionally called the present participle (forms such as
writing, singing and raising; these same forms also serve as gerunds
and verbal nouns), and the past participle (forms such as written,
sung and raised; regular participles such as the last, as well as some
irregular ones, have the same form as the finite past tense).
Also look under the "English" section of that article for some further explanation as well as a list of where each kind of participle can be used.
Hopefully it's clear now that you can't use "originated" in your sentence because it's not the case that "[some agent] originates local times". And you can't say "perpetuating" because it's not the case that "local times perpetuate [some patient]" (in addition, with these constructions, the prepositional phrases "from X" and "by Y" become nonsensical).