Abstract

In this paper a discrete dynamical system is considered . There is a dial with $N$ positions (vertices) and $M$ particles. Particles are located in vertices. Each particle moves, at every time unit, in accordance with its plan. The plan is logistics, given through a real number which belongs to the segment $[0,1].$ The number is represented in positional numeral system with base $N$ equal to the number of vertices. A competition takes place if particles must move in opposite directions simultaneously. A rule of competition resolution is given. Systems characteristics are investigated for sets of rational and irrational plans. Some algebraic constructions are introduced for this purpose. Probabilistic analogues (random walks) are also considered.

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