Flow spectrum of closed/open contours chains

Summary Dynamical systems with particle cluster flows on circles, forming a regular network structure can be used for analyzing transport flows, in biology (metabolism), in materials science (particles movement on periodic structures, for example in crystal lattices). A class of dynamical systems on regular contour graphs is studied in the paper. The study of closed and open chains of contours has revealed that there are structures such that, in a certain sense, these structures can be classified as Sturm‐Liouville‐type spectrum. In this paper, new analytical results have been obtained for contour networks that are closed or open chains of contours.