Geodesic
On attractors in one discrete binary dynamic system with bipartite dependency graph
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 163-165.

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One discrete binary dynamic system $(S_n,f)$, $n>1$, with bipartite dependency graph is considered. The states of such a system are all possible binary vectors of length $n$, and evolutionary function is $f=(x_n,0,\dots,0,x_1)$. In this case, $f$ is associated with a bipartite directed dependency graph with vertices set $\{a_1,\ldots,a_n,\epsilon\}$ and with arcs from $a_1$ to $a_n$, from $a_n$ to $a_1$ and from $a_i$ to $\epsilon$, $1$. The map of the $(S_3,f)$ system with the evolutionary function $f=(x_3,0,x_1)$ 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 $1$: $0^n$ and $10^{n-2}1$, and one attractor of length $2$ formed by states $00^{n-2}1$ and $10^{n-2}0$.
Keywords: attractor, basin, graph, dependency graph, discrete binary dynamic system, evolutionary function.
Mots-clés : bipartite graph 
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     title = {On attractors in one discrete binary dynamic system with bipartite dependency graph},
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R. I. Panteleev; A. V. Zharkova. On attractors in one discrete binary dynamic system with bipartite dependency graph. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 163-165. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a37/

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