ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Matrosov V. V., Shalfeev V. D. Coupled economic oscillations — synchronization dynamical model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 3, pp. 254-270. DOI: 10.18500/0869-6632-003037, EDN: INVKIQ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
Full text PDF(En):
Article type: 
338.12; 519.6; 530.182.2; 621.37

Coupled economic oscillations — synchronization dynamical model

Matrosov Valerij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Shalfeev Vladimir Dmitrievich, Lobachevsky State University of Nizhny Novgorod

Purpose of this work is the research of the dynamical processes and in particular the phenomenon of the synchronization in an ensemble of coupled chaotic economic oscillators.

Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations.

Results. The nonlinear model of economic oscillator as the system of automatic control are considered. Such kind of general economic models are unsuitable for getting some concrete economic estimations and recommendations. But such kind models are very useful for a development the theory of the economic cycles, theory of the generation, interactions, synchronization of the cycles and so on. Our numerical experiments demonstrated a good enough qualitative similarity of an chaotic economic oscillations in our model and real economic cycles.

The phenomen of the synchronization of the chaotic oscillations in the ensemble of coupled economic oscillators are considered, however the accuracy of the synchronization depends with couplings essentially.

This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. FSWR-2023-0031). Authors are grateful to M. I. Rabinovich and V. P. Рonomarenko for useful discussions and tips
  1. Samuelson P, Nordhaus W. Economics. 15th edition. New York: McGraw Hill; 1995. 792 p.
  2. Vechkanov GS, Vechkanova GR. Macroeconomics. Saint Petersburg: Piter; 2002. 412 p. (in Russian).
  3. Kuznetsov YA. Mathematical modeling of economic cycles: facts, concepts, results. Economic Analysis: Theory and Practice. 2011;10(17(224)):50–61 (in Russian).
  4. Kuznetsov YA. Mathematical modeling of economic cycles: facts, concepts, results (end). Economic Analysis: Theory and Practice. 2011;10(18(225)):42–56 (in Russian).
  5. Lebedeva AS. The genesis of the economic cycle theory. International Research Journal. 2013; 8–3(15):31–34 (in Russian).
  6. Lopes AM, Machado JAT, Huffstot JS, Mata ME. Dynamical analysis of the global business-cycle synchronization. PLoS ONE. 2018;13(2):e0191491. DOI: 10.1371/journal.pone.0191491.
  7. Oman W. The synchronization of business cycles and financial cycles in Euro area. International Journal of Central Banking. 2019;15(1):327–362.
  8. Guegan D. Chaos in economics and finance. Annual Reviews in Control. 2009;33(1):89–93. DOI: 10.1016/j.arcontrol.2009.01.002.
  9. Volos C, Kyprianidis I, Stouboulos IN. Synchronization phenomena in coupled nonlinear systems applied in economic cycles. WSEAS Transactions on Systems. 2012;11(12):681.
  10. Matrosov VV, Shalfeev VD. Simulation of business and financial cycles: Self-oscillation and synchronization. Izvestiya VUZ. Applied Nonlinear Dynamics. 2021;29(4):515–537 (in Russian). DOI: 10.18500/0869-6632-2021-29-4-515-537.
  11. Matrosov VV, Shalfeev VD. Simulation of the business-cycle synchronization processes in an ensemble of coupled economic oscillators. Radiophysics and Quantum Electronics. 2022;64(10): 750–759. DOI: 10.1007/s11141-022-10176-1.
  12. McCullen NJ, Ivanchenko MV, Shalfeev VD, Gale WF. A dynamical model of decision-making behavior in a network of consumers with applications to energy choices. International Journal of Bifurcation and Chaos. 2011;21(9):2467–2480. DOI: 10.1142/S0218127411030076.
  13. Ponomarenko VP. Modeling the evolution of dynamic modes in an oscillator system with frequency control. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;7(5):44–55 (in Russian).
  14. Ponomarenko VV, Zaulin IA. The dynamics of an oscillator controlled by a frequency-locked loop with an inverted discriminator characteristic. J . Commun. Technol. Electron. 1997;42(7):828–835 (in Russian).
  15. Kasatkin DV, Matrosov VV. Chaotic oscillations of two cascade-coupled oscillators with frequency control. Tech. Phys. Lett. 2006;32(4):357–360. DOI: 10.1134/S1063785006040250.
  16. Andronov AA, Vitt AA, Khaikin SE. Theory of Oscillators. New York: Dover Publications; 1987. 815 p.
  17. Belyakov LA. About structure of bifurcation multitudes in systems with separatrix loop of saddlefocus. In: Abstracts of the IX International Conference on Nonlinear Oscillations. Kiev: Institute of Mechanics of the Academy of Sciences of the Ukrainian SSR; 1981. P. 57 (in Russian).
  18. Schuler YS, Hiebert P, Peltonen TA. Characterising the financial cycle: a multivariate and time-varying approach. ECB Working Paper Series. No. 1846. Frankfurt am Main: European Central Bank; 2015. 54 p. DOI: 10.2139/ssrn.2664126.
  19. Shalfeev VD, Matrosov VV. Nonlinear Dynamics of Phase Synchronization Systems. Nizhny Novgorod: Nizhny Novgorod University Press; 2013. 366 p. (in Russian).
Available online: