The Bilingual Interaction Activation Plus (BIA+) model provides an insight into the brain of this population. It demonstrates that the two languages are stored in one integrated lexicon, with one separate node for each of them.
As both languages are constantly active in the bilingual's brain, they are pitted against each other when the individual is presented with linguistic input. That is, lexemes from the non-target language are co-activated and could potentially interfere with word recognition in the target language.
However, bilinguals can distinguish languages and choose the appropriate one. The reason they don’t mix them up is because the node pertaining to the non-target language is inhibited.
Language inhibition is affected by the strength of activation of the target language node. This finding is seen in lexical decision tasks in which participants are shown strings of letters and must decide as quickly as possible whether these form a real word or not.
Many studies conducted through these experiments have shown that words in different languages which share their origins (identical or non-identical cognates) are recognised faster by bilinguals, than those which don’t. This is known as the cognate facilitation effect. For example, Spanish-Italian bilinguals will take less time processing noche or notte (night in Spanish and Italian respectively) which are both derived from the Proto-Indo-European nókʷts, than cara or viso (face in Spanish and Italian).
In contrast, researchers have discovered that lexemes which share their orthography but not their meaning across languages (interlingual homographs) are harder to process and thus result in slower reaction times. As these words belong to the same nodes, they inhibit each other. This interlingual homograph inhibition effect can be seen in English-French bilinguals for instance, in the case of coin which means corner in French.
Although some specific questions about this population remain unanswered, our knowledge of this topic is continuously improving.