Spectrum of flows on discrete pair of contours

Abstract

We consider a deterministic discrete dynamical system, which is a contour network of Buslaev type. This system contains two contours. The ith contour contains Ni cells, i = 1, 2. There is a cluster of particles on each contour moving in accordance with given rules. The clusters contain 1 ≤ M1 < N1 and 1 ≤ M2 < N2 particles respectively. There is no more than one particle in each cell at any time. There is a common point (node) of the contours. Particles cannot cross the node simultaneously. A set of repeating system states is called a spectral cycle. Average velocities of clusters correspond to spectral cycles. The set of spectral cycles and values of the average velocities have been found.