Biderivations of some evolution algebras

The purpose of this paper is to prove that any biderivations of [Formula: see text]-dimensional complex evolution algebras depend on the rank of the appropriate matrices. For evolution algebras with nonsingular matrices, we prove that any biderivation is the zero mapping. All biderivations for evolution algebras with matrices of rank [Formula: see text] are described. Additionally, we characterize all biderivations of nilpotent [Formula: see text]-dimensional evolution algebras over an arbitrary field of characteristic zero.