Chain of evolution algebras of “chicken” population

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.