We present an original model designed to study how a second language (L2) is acquired in bilinguals at different proficiencies starting from an existing L1. The model assumes that the conceptual and lexical aspects of languages are stored separately: conceptual aspects in distinct topologically organized Feature Areas, and lexical aspects in a single Lexical Network. Lexical and semantic aspects are then linked together during Hebbian learning phases by presenting L2 lexical items and their L1 translation equivalents. The model hypothesizes the existence of a competitive mechanism to solve conflicts and simulate language switching tasks. Results demonstrate that, at the beginning of training, an L2 lexicon must parasitize its L1 equivalent to access its conceptual meaning. At intermediate proficiency, L2 items may evoke their semantics independently of L1, but with a high risk of interference. At higher proficiency, the L2 representation becomes progressively similar to the L1 representation, according to Green's (2003) convergence hypothesis.