This is Angela Friderici, a German expert in neuropsychology and linguistics. She believes that for bilingualism, the processes of particular language aspects are in the same brain area. When there is a dominant language and a non-dominant language, the non-dominant language will have more activation than the dominant language. The more automatic you can speak or listen to a language the less activation is seen in the brain because it is easier. Even though the level of activation is different for a dominant and non-dominant language they are in the same area of the brain.
She then discusses the problem with studying bilingualism and solutions to certain problems. When it comes to bilingual research it is really hard to control the particular constraint during language acquisition. Sometimes a dominant language may change overtime. For example, when I was around 4 or 5 years old my dominant language was Chinese but by the time I was 8 years old my dominant language became English. To deal with this problem lab studies would need a complete record of how a subject learned a language. Afterward a possible way to control the learning phase of language acquisition is to use an artificial grammar or a language they never learned before. An artificial grammar can be design anyway but should have grammatical rule of an actual grammar. Then they would examine certain aspects such as particular phonological aspects that are relevant language learning.
Bilingual Cognitive Development 