2013
DOI: 10.1134/s199508021304015x
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Dynamics of two-dimensional evolution algebras

Abstract: Recently in [2] 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 nilpoten… Show more

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Cited by 30 publications
(28 citation statements)
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“…In [1], [12] it were constructed several CEAs. Using these CEAs and the CEAs constructed in the previous sections, by Lemma 1 one can construct new chains of arbitrary dimensional evolution algebras, i.e.…”
Section: Ceas Corresponding To Block Diagonal Matricesmentioning
confidence: 99%
See 1 more Smart Citation
“…In [1], [12] it were constructed several CEAs. Using these CEAs and the CEAs constructed in the previous sections, by Lemma 1 one can construct new chains of arbitrary dimensional evolution algebras, i.e.…”
Section: Ceas Corresponding To Block Diagonal Matricesmentioning
confidence: 99%
“…. , n; e i e j = 0, i = j, In [12] 25 distinct examples of chains of two-dimensional evolution algebras are constructed. For all of chains constructed in [1] and [12] 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 are studied.…”
Section: Introductionmentioning
confidence: 99%
“…In [2], the authors studied the relationship between evolution algebras and the spaces of functions defined by the Gibbs measure of a graph, which led into direct applications in biology, physics and mathematics itself. In works such as [3][4][5][6][7][8][9][10] they studied purely mathematical notions, such as nilpotency and solvency of evolution algebras, as well as the interpretation of these mathematical notions, relating, for example, the nilpotency of an element to gametes that go extinct after some generations. Chains of evolution algebras were studied in [11][12][13][14].…”
Section: Introductionmentioning
confidence: 99%
“…Depending on the matrices, it can be a non-Markov process [4], a deformation [12], etc. Other motivations of consideration of non-stochastic solutions of KCE are given in recent papers [2,11,13,14,15]. These papers devoted to study some chains of evolution algebras.…”
Section: Introductionmentioning
confidence: 99%