Behavior of pendulums on a regular polygon

Stochastic and deterministic versions of a discrete dynamical network system are investigated. This network consists of a sequence of contours NSWE with nodes, which are common points at N, W, S and E. There are four cells and a particle on each contour. At each time instance, the particle occupies a cell, and attempts to occupy the next cell in the same direction. Particles of neighboring contours move in accordance with some rules. Both deterministic and stochastic rules are considered. The behavior of the model with the first rule is stochastic only at the beginning, and after a time interval the system becomes to pure deterministic. The system with the second rule comes to a steady state, which depends on the initial state. The average velocity of particles and other characteristics of the system are studied.