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Chain of evolution algebras of “chicken” population

Authors
  • Rozikov, U.A.
  • Murodov, Sh.N.1
  • 1 Institute of Mathematics
Type
Published Article
Journal
Linear Algebra and its Applications
Publisher
Elsevier
Publication Date
Jan 01, 2014
Accepted Date
Mar 03, 2014
Volume
450
Pages
186–201
Identifiers
DOI: 10.1016/j.laa.2014.03.001
Source
Elsevier
Keywords
License
Unknown

Abstract

Recently Ladra and Rozikov introduced a notion of evolution algebra of a “chicken” population (EACP). The algebra is given by a rectangular matrix of structural constants. In this paper we introduce a notion of chain of evolution algebras of a “chicken” population (CEACP). The sequence of matrices of the structural constants for this CEACP satisfies an analogue of Chapman–Kolmogorov equation (with a specific multiplication defined for rectangular matrices). We give several examples (time homogeneous, time non-homogeneous, periodic, etc.) of such chains. We construct some periodic 3-dimensional CEACP which contains a continuum set of non-isomorphic EACP and show that the corresponding discrete time CEACP is dense in the set. Moreover we study time depending dynamics of 2 and 3 dimensional CEACP to be isomorphic to a fixed algebra.

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