Bifurcation Analysis and Synergetic Management of the Dynamic System “Intermediary Activity”

  • Alexander V. Bratishchev
  • Galina A. BatishchevaEmail author
  • Maria I. Zhuravleva
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 896)


The full bifurcation analysis of the mathematical model of the dynamic system “Intermediary activity” proposed by V. P. Milovanov is carried out in the article. Using the poincaré transform, the behavior of trajectories at infinity is investigated. Two logically possible phase portraits of the system were obtained using theoretical analysis and numerical experiment in the Matlab package. The system of additive control of both cash and commodity flows is constructed by the method of analytical construction of aggregated regulators to achieve a given dynamic equilibrium from an arbitrary initial state. Dedicated class a valid reachable States. The stability of such state as a whole is proved. This model makes it possible to predict the development of the process for any given initial state of the system in advance, as well as to control the parameters of the system for designing a given dynamic equilibrium in advance.


Cash and commodity flows Autonomous system Equilibrium state Phase portrait Parameter space Asymptotic stability Aggregated variable 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander V. Bratishchev
    • 1
  • Galina A. Batishcheva
    • 2
    Email author
  • Maria I. Zhuravleva
    • 2
  1. 1.Don State Technical UniversityRostov-on-DonRussia
  2. 2.Rostov State University of EconomicsRostov-on-DonRussia

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