Stability of Flows on Networks.

The problems of traffic flow forecasting on complex traffic networks are still almost not explored. However these problems are very actual for scientists as well as for traffic engineers. In this paper we consider problems of stability of particle (car) flows on networks. The definitions of critical, stable and unstable flow states on networks are obtained as properties of solutions of nonlinear differential equations on graphs. For networks with different geometry the necessary and sufficient conditions of flow stability on networks are found. The perspective problems of exploration of qualitative properties of flows on networks are formulated. [ABSTRACT FROM AUTHOR]