Bifurcation in the Model of Cargo Transportation Organization

Abstract

This article is devoted to the study of the model of cargo transportation organization between two nodal stations. The main characteristic of an arbitrary station is the degree of inconsistency between receiving and sending cargo, which is the difference between the volume of incoming and outgoing cargo per unit of time. The initial node station accepts goods depending on the demand for them within its technical potential, which is determined by the maximum allowable increase in the degree of inconsistency between the reception and dispatch of goods per unit of time. The movement of goods from one station to another is carried out within the framework of their technical potentials. The distribution of goods from the final node station is carried out in a certain mode. Such a model is described by a system of differential equations with a number of parameters that define the characteristics of the demand for cargo transportation, the degree of use of the technical potential of the stations and the mode of cargo distribution from the final node station. When changing the parameters of the model, a bifurcation effect occurs and multiple stationary solutions appear, among which the most acceptable from the point of view of economic feasibility are identified.