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This work classifies three-dimensional simple evolution algebras overarbitrary fields. For this purpose, we use tools such as the associateddirected graph, the moduli set, inductive limit group, Zariski topology and thedimension of the diagonal subspace. Explicitly, in the three-dimensional case,we construct some models $_i\mathbf{III}_{\lambda_1,\ldots,\lambda_n}^{p,q}$ ofsuch algebras with $1\le i\le 4$, $\lambda_i\in\mathbb{K}^\times$,$p,q\in\mathbb{N}$, such that any algebra is isomorphic to one (and only one)of the given in the models and we further investigate the isomorphic questionwithin each one. Moreover, we show how to construct simple evolution algebrasof higher-order from known simple evolution algebras of smaller size.

On simple evolution algebras of dimension two and three. Constructing simple and semisimple evolution algebras