Bifurcation Analysis and Synergetic Control of a Dynamic System with Several Parameters

摘要

The article provides a complete bifurcation analysis of the mathematical model of the dynamic system "Emergence of planned regulation" proposed by V. P. Milovanov. The behavior of trajectories at infinity is studied using the Poincare transform. With the help of theoretical analysis and numerical experiment the phase portrait of the system is obtained in Matlab package. The system turned out to be a lip in the open first quarter of the phase plane. The system of additive control of both cash and commodity flows to achieve a given dynamic equilibrium from an arbitrary initial state is constructed by the method of analytical design of aggregated regulators. Dedicated class a valid reachable States. The numerical experiment shows the stability of this state as a whole. This model allows you to predict the development of the process for any predetermined initial state of the system, as well as to control the parameters of the system to design a predetermined dynamic equilibrium.