Term for emergent system with its own logical rules/laws?
In psychology, implicit may be the word. It means 'before conscious thought takes place' or 'inherent to the organism', but as a result of conditioning, rather than by instinct alone. You can learn more about this at Project Implicit®.
I would suggest the term autonomous, coming from latin terms that point exactly to the same meaning as your referred Eigenlogik, and being currently used in different scientific and philosophic disciplines concerned with (broadly defined) agency.