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Monotonic walks on a necklace and a coloured dynamic vector. (English) Zbl 1342.37059
Summary: Stochastic and deterministic versions of a discrete dynamical system on a necklace are investigated. This network consists of a sequence of contours NSWE with nodes, i.e. the nodes are common points at $$W$$ and $$E$$. There are two cells and a particle on each contour. Each time instance, the particle occupies a cell and, at every time unit, comes to the next cell in the same direction. The particles of the neighbouring contours move in accordance with rules of stochastic or deterministic type. The behaviour of the model with the rule of the first type is stochastic only at the beginning and after a time interval becomes a pure deterministic system. The system with the second rule comes to a steady mode, which depends on the initial state. The average velocity of particles and characteristics of the system are studied.

##### MSC:
 37H99 Random dynamical systems 37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems 60G50 Sums of independent random variables; random walks
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