About Synergy of Flows on Flower

Classical traffic flow theory was broadly separated into two branches: fluid-dynamical approach and and car-following micromodelling, and most important and difficult problems are network modelling of traffic flow. There exist many works of experimental and computer simulation types, but exact results fot saturated traffic flow on networks are appeared not often. We consider a movement of particles on network of special type as a set of contours with a common node. In 2009 we introduced a flower as network type for transport model, where the dynamical system defined by a system of differential equations on flower was developed. In this paper we study, for the system of connected contours, problem of search the conditions, such that the system becomes synergy mode independence on initial particles configuration at finite time, i.e. all particles move without delay for next time. It is proved, besides all the other results, that the search of synergy conditions is reduced to the investigation of the existence of solutions of linear Diophantine equations with two variables.