I like the both Apple and Google user experiences. But visually they are different. Though, I need to know their basic concepts/theory about user experience.
So we will take their inspirations not copying.
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Yes there is.
Android UX Guidelines: http://developer.android.com/guide/practices/ui_guidelines/index.html
The Basic Concepts - are actually covered on in this part of the Apple UX Guidelines.
They used to explain this in more detail - and it's got cut down over time.
Originally there was a very handy reading list, which used to list all the academic research which supported the interface design. (takes a while to load as its on the Wayback Machine)