Spectrum of continuous two-contours system

Abstract

A deterministic continuous dynamical system is considered. This system contains two contours. The length of the ith contour equals ci, i = 1, 2. There is a moving segment (cluster) on each contour. The length of the cluster, located on the ith contour, equals li , i = 1, 2. If a cluster moves without delays, then the velocity of the cluster is equal to 1. There is a common point (node) of the contours. Clusters cannot cross the node simultaneously, and therefore delays of clusters occur. A set of repeating system states is called a spectral cycle. Spectral cycles and values of average velocities of clusters have been found. The system belongs to a class of contour systems. This class of dynamical systems has been introduced and studied by A.P. Buslaev.