Here are some links to information about possessives and articles.:
Well.. I dont know if there is a rule, I asked portuguese friends of mine and they didnt know a rule... Their explanation attempt was sth like this:
If your birds eat bread (meaning some bread): no article If your birds eat THE bread you just put there to feed them: article
So kinda like in english... I eat rice = Eu como arroz I eat THE rice you made = eu como o arroz ...
Id really appreciate a rule though. ;)
Let me try to explain: In brasilian portuguese, we can use or not the article before possessive pronaums. Look.
(Without article) -PT: [Pergunta] De quem é este carro? [Resposta simples] MEU. [Resposta completa] Este carro é MEU. - EN: [Question] Whose is this car? [Short answer] Mine. (I don't know if in english is usualy to answer this way) [Full answer] This car is mine.
(With article) -PT: [Pergunta] Qual carro? [Resposta simples] O MEU. [Resposta completa] O MEU carro. -EN: [Question] Wich car? [Short answer] Mine. [Full answer] My car.
I realy hope I've been helpfull. Any doubts?