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Delayed feedback on the dynamical model of a financial system

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  • Son, Woo-Sik
  • Park, Young-Jai

Abstract

We investigate the effect of delayed feedbacks on the financial model, which describes the time variation of the interest rate, the investment demand, and the price index, for establishing the fiscal policy. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Through numerical bifurcation analysis, we obtain the supercritical and subcritical Hopf bifurcation curves which support the theoretical predictions. Moreover, the fold limit cycle and Neimark–Sacker bifurcation curves are detected. We also confirm that the double Hopf and generalized Hopf codimension-2 bifurcation points exist.

Suggested Citation

  • Son, Woo-Sik & Park, Young-Jai, 2011. "Delayed feedback on the dynamical model of a financial system," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 208-217.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:4:p:208-217
    DOI: 10.1016/j.chaos.2011.01.010
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    1. Chian, Abraham C.-L. & Borotto, Felix A. & Rempel, Erico L. & Rogers, Colin, 2005. "Attractor merging crisis in chaotic business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 869-875.
    2. Ma, Junhai & Sun, Tao & Liu, Lixia, 2008. "The inherent complexity in nonlinear business cycle model in resonance," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1104-1112.
    3. Neamţu, Mihaela & Opriş, Dumitru & Chilaˇrescu, Constantin, 2007. "Hopf bifurcation in a dynamic IS–LM model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 519-530.
    4. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    5. De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
    6. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    7. Fanti, Luciano & Manfredi, Piero, 2007. "Chaotic business cycles and fiscal policy: An IS-LM model with distributed tax collection lags," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 736-744.
    8. Hołyst, Janusz A & Urbanowicz, Krzysztof, 2000. "Chaos control in economical model by time-delayed feedback method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 587-598.
    9. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
    10. Ma, Junhai & Cui, Yaqiang & Liulixia,, 2009. "A study on the complexity of a business cycle model with great excitements in non-resonant condition," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2258-2267.
    11. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
    12. J.A. Hołyst & M. Żebrowska & K. Urbanowicz, 2001. "Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy?," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 531-535, April.
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