On attractors in one discrete binary dynamic system with bipartite dependency graph

One discrete binary dynamic system (Sn, f), n > 1, with bipartite dependency graph is considered. The states of such a system are all possible binary vectors of length n, and evolutionary function is f = (xn, 0, . . . , 0, x1). In this case, f is associated with a bipartite directed dependency graph with vertices set {a₁,... ,a_n,e} and with arcs from a₁ to a_n, from a_n to a₁ and from a_i to e, 1 < i < n. The map of the (S₃, f) system with the evolutionary function f = (x3, 0, x1) and its bipartite dependency graph are presented. A theorem is given on the type and number of attractors in these systems. Namely, the system has two attractors of length 1: 0ⁿ and 10^n-21, and one attractor of length 2 formed by states 00^n-21 and 10^n-20.

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