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Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model

Author

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  • IRINA BASHKIRTSEVA

    (Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 6200000, Russia)

  • ALEXANDER PISARCHIK

    (Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150 Leon, Guanajuato, Mexico3Computational Systems Biology, Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain)

  • LEV RYASHKO

    (Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 6200000, Russia)

  • TATYANA RYAZANOVA

    (Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 6200000, Russia)

Abstract

Stochastically forced business cycle model is considered. We study a phenomenon of the noise-induced generation of complex mixed-mode oscillations in zones where the deterministic model exhibits a single attractor (equilibrium or limit cycle). A probabilistic mechanism of the transition from unimodal oscillations to the intermittency of small- and large-amplitude stochastic oscillations is investigated on the base of the stochastic sensitivity functions technique. We show that such intermittency, connected with the nonuniformity of phase portrait, can be parametrically analyzed by the confidence domains method.

Suggested Citation

  • Irina Bashkirtseva & Alexander Pisarchik & Lev Ryashko & Tatyana Ryazanova, 2016. "Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-16, February.
    • Handle: RePEc:wsi:acsxxx:v:19:y:2016:i:01n02:n:s0219525915500277
    DOI: 10.1142/S0219525915500277
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    References listed on IDEAS

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    1. Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
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    3. Bashkirtseva, Irina & Ryazanova, Tatyana & Ryashko, Lev, 2015. "Analysis of dynamic regimes in stochastically forced Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 96-104.
    4. Domenico Delli Gatti & Corrado Di Guilmi & Edoardo Gaffeo & Gianfranco Giulioni & Mauro Gallegati & Antonio Palestrini, 2004. "Business Cycle Fluctuations And Firms’ Size Distribution Dynamics," World Scientific Book Chapters, in: Roberto Leombruni & Matteo Richiardi (ed.), Industry And Labor Dynamics The Agent-Based Computational Economics Approach, chapter 10, pages 199-221, World Scientific Publishing Co. Pte. Ltd..
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    6. Bashkirtseva, Irina & Ryashko, Lev, 2013. "Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 295-306.
    7. Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.
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