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A chain of evolution algebras (CEA) is an uncountable family (depending on time) of evolution algebras on the field of real numbers. The matrix of structural constants of a CEA satisfies the Chapman-Kolmogorov equation. In this paper, we consider three CEAs of three-dimensional real evolution algebras. These CEAs depend on several (non-zero) functions defined on the set of time. For each chain we give a full classification (up to isomorphism) of the algebras depending on the time-parameter. We find concrete functions ensuring that the corresponding CEA contains all possible three-dimensional evolution algebras. [ABSTRACT FROM AUTHOR]

Motivated by the China's five element philosophy (CFEP), we construct a permuted Volterra quadratic stochastic operator acting on the four-dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution operator for CFEP. We study the discrete-time dynamical system generated by this operator. Mainly our results related to a symmetric operator (depending on one parameter). We show that this operator has a unique fixed point, which is repeller. Moreover, in the case of non-zero parameter, it has two 5-periodic orbits. We divide the simplex to four subsets: the first set consists a single point (the fixed point); the second (resp. third) set is the set of initial point trajectories of which converge to the first (resp. second) 5-periodic orbit; the fourth subset is the set of initial point trajectories of which do not converge and their sets of limit points are infinite and lie on the boundary of the simplex. We give interpretations of our results to CFEP. [ABSTRACT FROM AUTHOR]

We consider algebras of-cubic matrices (with). Since there are several kinds of multiplications of cubic matrices, one has to specify a multiplication first and then define an algebra of cubic matrices (ACM) with respect to this multiplication. We mainly use the associative multiplications introduced by Maksimov. Such a multiplication depends on an associative binary operation on the set of sizem. We introduce a notion of equivalent operations and show that such operations generate isomorphic ACMs. It is shown that an ACM is not baric. An ACM is commutative iff. We introduce a notion of accompanying algebra (which is-dimensional) and show that there is a homomorphism from any ACM to the accompanying algebra. We describe (left and right) symmetric operations and give left and right zero divisors of the corresponding ACMs. Moreover several subalgebras and ideals of an ACM are constructed. [ABSTRACT FROM AUTHOR]

In this article, we describe a wide class of non-Volterra quadratic stochastic operators using N. Ganikhadjaev's construction of quadratic stochastic operators. By the construction these operators depend on a probability measure μ being defined on the set of all configurations which are given on a graph G. We show that if μ is the product of probability measures being defined on each maximal connected subgraphs of G then corresponding non-Volterra operator can be reduced to m number (where m is the number of maximal connected subgraphs of G) of Volterra operators defined on the maximal connected subgraphs. Our result allows to study a wide class of non-Volterra operators in the framework of the well known theory of Volterra quadratic stochastic operators. [ABSTRACT FROM AUTHOR]