Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bratishchev, A.V., Batishcheva, G.A., Zhuravleva, M.I.: Bifurcation analysis and synergetic management of the dynamic system “intermediary activity”. In: Proceedings of 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing, ICAFS-2018. Advances in Intelligent Systems and Computing. AISC, vol. 896, pp. 659–667 (2018)
Bautin, N.N., Leontovich, E.A.: Methods of qualitative research of dynamic systems on a plane. Ed.2, Moscow, Science (1990)
Kolesnikov, A.A.: Synergetic Methods of Control of Complex Systems. The Theory of System Analysis. Komkniga, Moscow (2006)
Milovanov, V.P.: Synergetics and Self-organization. Economy. Biophysics. Komkniga, Moscow (2005)
Demidovich, B.P.: Lectures on Mathematical Theory of Stability. LAN Publishing House, St. Petersburg (2008)
Lazarev, Yu.: Modeling Processes and Systems in MATLAB. Publishing Group BHV, Peter, Kiev (2005)
Bratishchev, A.V.: On the characteristic polynomial of the equilibrium state of an Autonomous system having an attractive invariant variety. Differ. Equ. Control Process. 2, 15–23 (2017)
Zubov, V.I.: Stability of Motion. Vysshaya SHKOLA, Moscow (1973)
Bratishchev, A.V.: The Mathematical Theory of Controlled Dynamical Systems. Introduction to Concepts and Methods. Publishing Center DGTU, Rostov-on-Don (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Bratishchev Alexander, V., Batishcheva Galina, A., Denisov Mikhail, Y., Zhuravleva Maria, I. (2020). Bifurcation Analysis and Synergetic Control of a Dynamic System with Several Parameters. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, vol 1095. Springer, Cham. https://doi.org/10.1007/978-3-030-35249-3_82
Download citation
DOI: https://doi.org/10.1007/978-3-030-35249-3_82
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35248-6
Online ISBN: 978-3-030-35249-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)