Ergodicity invariance under isomorphism of Volterra evolution algebras

Let ${\mathcal E}_1$ and ${\mathcal E}_2$ be two $n$-dimensional isomorphic Volterra evolution algebras, and let the corresponding Volterra quadratic stochastic operators be the operators associated with these algebras. Ergodicity invariance conjecture. The two corresponding Volterra quadratic stochastic operators are either both ergodic or both non-ergodic. The paper proves this assertion in the three-dimensional setting, but the proposed extension to arbitrary dimension $n$ is not resolved in the supplied text.