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The paper considers a discrete dynamical system containing two contours. There are n cells and m particles in each contour. At any time, the particles of each contour form a cluster. There are two common points of the contours. These common points are called nodes. The nodes divide the contours into two nonequal parts. The system belongs to the class of dynamical systems introduced by A. P. Buslaev. In these systems, the movement of particles (clusters) can be interpreted as the mass transfer on regular networks. A cyclic trajectory in the system state space is called a spectral cycle. The system state space is divided into sets such that any of this set contains the states of the spectral cycle and the nonrecurrent states from which the system results in the set of the spectral cycle states. We have found that, in the general case, what spectral cycle is realized and with what average velocity the clusters move depends on the initial state of the system. We have found the set of spectral cycles and the values of the clusters average velocities taking into account the delays due to that the clusters cannot pass through the same node simultaneously. In one of two considered versions of the system, the clusters move counterclockwise (one‐directional movement). In the other version, one of the clusters moves clockwise and the other cluster moves counterclockwise (codirectional movement). It is turned out that the behavior of system is significantly different in these versions. In particular, in the case of the codirectional movement, the average clusters velocity does not depend on the initial state.

Abstract. Considered dynamical system is a flow of clusters with the same length l on contours of unit length connected in polar-remote points into closed chain. When clusters move through common node, the left-priority rule of competition resolution works. In the paper it is shown that, in the case of chain containing three contours, the dynamical system has a spectrum of velocity and mode periodicity consisted of not more than two components. Spectrum distribution in dependence on load l is developed. Hypotheses on discrete spectrum in the case of arbitrary number of contours are formulated.

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