Dynamics of two-dimensional evolution algebras
U. A. Rozikov, Sh. N. Murodov
TL;DR
This paper constructs and analyzes 25 examples of two-dimensional evolution algebra chains, exploring their properties over time, including baric property, nilpotent elements, and idempotent dynamics.
Contribution
It provides explicit examples of evolution algebra chains and studies their dynamic properties, extending understanding of their temporal behavior.
Findings
Behavior of baric property over time
Dynamics of nilpotent elements
Evolution of idempotent elements
Abstract
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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Topics in Algebra · Fractional Differential Equations Solutions