A Two-Contour System with Two Clusters of Different Lengths

Abstract

A system belonging to the class of dynamical systems such as Buslaev contour networks is investigated. On each of the two closed contours of the system there is a segment, called a cluster, which moves with constant velocity if there are no delays. The contours have two common points called nodes. Delays in the motion of the clusters are due to the fact that two clusters cannot pass through a node simultaneously. The main characteristic we focus on is the average velocity of the clusters with delays taken into account. The contours have the same length, taken to be unity. The nodes divide each contour into parts one of which has length d, and the other, length 1-d. Previously, this system was investigated under the assumption that the clusters have the same length. It turned out that the behavior of the system depends qualitatively on how the directions of motion of the clusters correlate with each other. In this paper we explore the behavior of the system in the case where the clusters differ in length.