Time depending dynamics of chains of evolution algebras

Abstract

This thesis is devoted to study the time‐depending dynamics of chains of evolution algebras (CEAs). Such chains are dynamical systems whose states, at each moment, are evolution algebras. The sequences of matrices of the structural constants of the CEAs satisfy the Chapman‐Kolmogorov equation. We construct new two‐dimensional real CEAs, study their property transitions and obtain their classification. We also define (linear) Rota‐Baxter operators on evolution algebras. Finally, we construct CEAs of "chicken" population, and study the time‐depending dynamics of such constructed CEAs.