Geodesic
Functioning of discrete dynamic circulant-type system with threshold functions
Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 84-95

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The functioning of discrete dynamic circulant-type systems with threshold functions is studied. The general properties of the functional graph of a system are described. In binary case, all states of the system are classified according to the length of $0$-series and $1$-series. As a result, some properties of cycles in the functional graph and a lower estimate for the number of connected components are given. For an arbitrary value $p$, a criterion for the existence of stable states in the system is given, the forms and the number of these states are determined.
Keywords: discrete dynamic systems, functional graph, threshold functions, cycles of functional graph, stable states.
Mots-clés : circulant graph 
@article{PDM_2014_4_a9,
     author = {I. S. Bykov},
     title = {Functioning of discrete dynamic circulant-type system with threshold functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {84--95},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_4_a9/}
}
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I. S. Bykov. Functioning of discrete dynamic circulant-type system with threshold functions. Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 84-95. http://geodesic.mathdoc.fr/item/PDM_2014_4_a9/