# Chain of evolution algebras of “chicken” population

- Authors
- 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.