Discrete two-contour system with co-directional movement

Abstract

The paper studies a discrete dynamical system, which belongs to the class of contour systems developed by A.P Buslaev. The system contains two closed contours. There are n cells and a group of particles at each contour. This group is called a cluster. The particles of a cluster are in adjacent cells and move simultaneously. At each discrete moment any particle moves onto a cell in the direction of movement. There are two common points of contours called nodes. Delays of clusters occur at the nodes. These delays are due to that two particles cannot cross the same node simultaneously. Earlier this system were studied under the assumptions that the number of particles does not depend on the cluster. This paper studies a system with different lengths of clusters. Analytical results are obtained for limit cycles of the system and the spectrum of average cluster velocities.