Spectra of Local Cluster Flows on Open Chain of Contours (European Journal of Pure and Applied Mathematics, 2018)
A dynamical system is considered. This dynamical system is a flow of clusters with the same length $l$ on contours of unit length connected into open chain. A similar system such that contours of this system are connected into closed chain was considered earlier. It has been found that, in the case of closed chain of contours, the dynamical system has a spectrum of velocity and mode periodicity consisted of more than one component. In this paper, it has been shown that, in the case of open chain, the spectrum of cluster velocity and mode periodicity contains only one component.The conditions of self-organization and the dependence of cluster velocity on load $l$ is developed.
Keywords: Dynamical System; Spectrum; Self-Organization; Contour Graph; Cluster Model