  Recently by Casas, Ladra and Rozikov a notion of a chain of evolution
algebras is introduced. This chain is a dynamical system the state of which at
each given time is an evolution algebra. The sequence of matrices of the
structural constants for this chain of evolution algebras satisfies the
Chapman-Kolmogorov equation. In this paper we construct 25 distinct examples of
chains of two-dimensional evolution algebras.
  For all of these 25 chains we study the behavior of the baric property, the
behavior of the set of absolute nilpotent elements and dynamics of the set of
idempotent elements depending on the time.
