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

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Matrosov V. V., Shalfeev V. D. Simulation of business and financial cycles: Self-oscillation and synchronization. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 4, pp. 515-537. DOI: 10.18500/0869-6632-2021-29-4-515-537

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338.12; 519.6; 530.182.2; 621.37

Simulation of business and financial cycles: Self-oscillation and synchronization

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

The purpose of this work is to research the phenomena of the self-oscillation and the synchronization for the model of business and financial oscillator, which presented as the system of automatic control. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. This work presents the model of business and financial oscillators as the phase-controlled oscillator and as the frequency-controlled oscillator. The phenomena of the self-oscillation of regular and chaotic oscillations in this model and the synchronization of such oscillations are considered.

The work was carried out within the framework of the Program for the Development of the Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, project № 075-02-2020-1483/1, and with the support of the Ministry of Education and Science of the Russian Federation within the framework of the state task (agreement 0729-2020-0040). The authors are grateful to M. I. Rabinovich for drawing attention to this topic, useful comments and tips on work
  1. Motova MI, Shalfeev VD. From theory of oscillations to nonlinear dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics. 2014;22(1):93–103 (in Russian). DOI: 10.18500/0869-6632-2014-22-1-93-103.
  2. Weidlich W. Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences. CRC Press; 2000. 392 p.
  3. Neimark YI. Mathematical Models in Natural Science and Technology. Nizhny Novgorod: Publishing House of Nizhny Novgorod University; 2004. 401 p. (in Russian).
  4. Koronovskii AA, Trubetskov DI. Nonlinear Dynamics in Action. How Ideas of Nonlinear Dynamics Penetrate Ecology, Economics and Social Sciences. The 2nd edition. Saratov: «College»; 2002. 322 p. (in Russian).
  5. Kuznetsov YA. Mathematical modeling of economic cycles: facts, concepts, results. Economic Analysis: Theory and Practice. 2011;10(17–18) (in Russian).
  6. Weinstock LR. Introduction to U.S. Economy: The Business Cycle and Growth. CRS In Focus. No. IF 10411. July 31, 2020. Washington, D.C.: Congressional Research Service; 2020.
  7. Drehmann M, Borio C, Tsatsaronis K. Characterising the financial cycle: don’t lose sight of the medium term! BIS Working Papers. No. 380. Basel: Bank for International Settlements; 2012. 37 p.
  8. Baxter M, King RG. Measuring business cycles: Approximate band-pass filter for economic time series. The Review of Economics and Statistics. 1999;81(4):575–593. DOI: 10.1162/003465399558454.
  9. Creal D, Koopman SJ, Zivot E. Extracting a robust US business cycle using a time-varying multivariate model-based bandpass filter. Journal of Applied Econometrics. 2010;25(4):695–719. DOI: 10.1002/jae.1185.
  10. Volos CK, Kyprianidis IM, Stouboulos IN. Synchronization phenomena in coupled nonlinear systems applied in economic cycles. WSEAS Transaction on Systems. 2012;11(12):681.
  11. Ulasenka M, Yuzefalchik I. Financial market and real sector of the economy: Interrelation and transmission of shocks. Banking Bulletin. 2018;(12(665)):9–17 (in Russian).
  12. Goodwin RM. A Growth Cycle. Cambridge: Cambridge University Press; 1967.
  13. Bouali S. Feedback loop in extended Van der Pol’s equation applied to an economic model of cycles. International Journal of Bifurcation and Chaos. 1999;9(4):745–756. DOI: 10.1142/S0218127499000535.
  14. Guegan D. Chaos in economics and finance. Annual Reviews in Control. 2009;33(1):89–93. DOI: 10.1016/j.arcontrol.2009.01.002.
  15. Schuler YS, Hiebert PP, 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.
  16. Schuler YS, Hiebert P, Peltonen T. Coherent financial cycles for G-7 countries: Why extending credit can be asset. ESRB Working Paper Series. No. 43. Frankfurt am Main: European Systemic Risk Board; 2017. 42 p. DOI: 10.2849/872841.
  17. Galati G, Hindrayanto I, Koopman SJ, Vlekke M. Measuring financial cycles with a model-based filter: Empirical evidence for the United States and the euro area. DNB Working Papers. No. 495. Amsterdam: Netherlands Central Bank; 2016.
  18. Avouyi-Dovi S, Matheron J. Interactions between business cycles, financial cycles and monetary policy: stylised facts. BIS Papers. No. 22. Basel: Bank for International Settlements; 2005. P. 273–298.
  19. Claessens S, Kose MA, Terrones ME. How do business and financial cycles interact? Journal of International Economics. 2012;87(1):178–190. DOI: 10.1016/j.jinteco.2011.11.008.
  20. Oman W. The synchronization of business cycles and financial cycles in Euro area. International Journal of Central Banking. 2019;15(1):327–362.
  21. Harding D, Pagan A. A comparison of two business cycle dating methods. Journal of Economic Dynamics and Control. 2003;27(9):1681–1690. DOI: 10.1016/S0165-1889(02)00076-3.
  22. 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.
  23. Granville B, Hussain S. Eurozone cycles: An analysis of phase synchronization. International Journal of Finance and Economics. 2017;22(2):83–114. DOI: 10.1002/ijfe.1576.
  24. Mosekilde E, Larsen ER, Sterman JD, Thomsen JS. Mode locking and nonlinear entrainment of macroeconomic cycles. In: Day RH, Chen P, editors. Nonlinear Dynamics and Evolutionary Economics. New York: Oxford University Press; 1993. P. 58–83.
  25. Mosekilde E, Larsen ER, Sterman JD, Thomsen JS. Nonlinear mode-interaction in the macroeconomy. Annals of Operations Research. 1992;37(1):185–215. DOI: 10.1007/BF02071056.
  26. Mosekilde E, Thomsen JS, Sterman J. Nonlinear Interactions in the Economy. In: Haag G, Mueller U, Troitzsch KG, editors. Economic Evolution and Demographic Change. Berlin: Springer; 1992. P. 35–61. DOI: 10.1007/978-3-642-48808-5_2.
  27. Selover DD, Jensen RV. ’Mode-locking’ and international business cycle transmission. Journal of Economic Dynamics and Control. 1999;23(4):591–618. DOI: 10.1016/S0165-1889(98)00036-0.
  28. Sussmuth B. Modeling the synchronization of sectoral investment cycles on the base of informational externalities. Structural Change and Economic Dynamics. 2003;14(3):35–54. DOI: 10.1016/S0954-349X(02)00048-6.
  29. Selover DD, Jensen RV, Kroll J. Mode-locking and regional business cycle synchronization. Journal of Regional Science. 2005;45(4):703–745. DOI: 10.1111/j.0022-4146.2005.00390.x.
  30. Sussmuth B, Woitek U. Some new results on industrial sector mode-locking and business cycle formation. Studies in Nonlinear Dynamics and Econometrics. 2005;9(3):1–33. DOI: 10.2202/1558- 3708.1185.
  31. Filer L, Selover DD. Why can weak linkages cause international stock market synchronization? The mode-locking effect. International Journal of Financial Research. 2014;5(3):20–42. DOI: 10.5430/ijfr.v5n3p20.
  32. Zheng S. Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems. Kybernetika. 2016;52(2):241–257. DOI: 10.14736/kyb-2016-2-0241.
  33. Zhang W, Cao J, Alsaedi F, Alsaadi FES. Synchronization of time delayed fractional order chaotic financial system. Discrete Dynamics in Nature and Society. 2017;2017:1230396. DOI: 10.1155/2017/1230396.
  34. Gardini L, Cori L, Guerrini L, Sodini M. Introduction to the focus issue “nonlinear economic dynamics”. Chaos. 2018;28(5):055801. DOI: 10.1063/1.5039304.
  35. Kapranov MV. Elements of the Theory of Phase Synchronization Systems. Moscow: MPEI Publishing House; 2006. 208 p. (in Russian).
  36. Shalfeev VD, Matrosov VV. Nonlinear Dynamics of Phase Synchronization Systems. Nizhny Novgorod: Publishing House of Nizhny Novgorod University; 2013. 366 p. (in Russian).
  37. Matrosov VV. Regular and chaotic self-oscillations of the phase system. Tech. Phys. Lett. 1996;22(23):4–8.
  38. Matrosov VV. Regular and chaotic oscillations in the phase system. Vestnik of Lobachevsky University of Nizhni Novgorod. Nonlinear Dynamics – Synchronization and Chaos-II. 1997:53–64.
  39. Matrosov VV. Nonlinear dynamics of phase-locked loop with the second-order filter. Radiophys. Quantum Electron. 2006;49(3):239–249. DOI: 10.1007/s11141-006-0057-6.
  40. McCullen NJ, Ivanchenko MV, Shalfeev VD, Gale WF. A dynamical model of decision-making behaviour 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
  41. Ponomarenko VP. Modeling the evolution of dynamic modes in an oscillator system with frequency control. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(5):44–55 (in Russian).
  42. Ponomarenko VP, 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.