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Attractor merging crisis in chaotic business cycles

Author

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  • Chian, Abraham C.-L.
  • Borotto, Felix A.
  • Rempel, Erico L.
  • Rogers, Colin

Abstract

A numerical study is performed on a forced-oscillator model of nonlinear business cycles. An attractor merging crisis due to a global bifurcation is analyzed using the unstable periodic orbits and their associated stable and unstable manifolds. Characterization of crisis can improve our ability to forecast sudden major changes in economic systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:3:p:869-875
    DOI: 10.1016/j.chaos.2004.09.080
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    Cited by:

    1. Solari, Hernán G. & Natiello, Mario A., 2009. "The topological reconstruction of forced oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2023-2034.
    2. Volos, Ch. K. & Kyprianidis, I.M. & Stouboulos, I.N. & Vaidyanathan, S. & Pham, V.-T., 2016. "Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemAuthor-Name: Tacha, O.I," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 200-217.
    3. Li, Jiaorui & Feng, C.S., 2010. "First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5557-5562.
    4. 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.
    5. Saiki, Y. & Chian, A.C.L. & Yoshida, H., 2011. "Economic intermittency in a two-country model of business cycles coupled by investment," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 418-428.
    6. 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.
    7. 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.
    8. Elliott, Robert J. & Chen, Zhiping & Duan, Qihong, 2009. "Insurance claims modulated by a hidden Brownian marked point process," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 163-172, October.
    9. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    10. A. C. -L. Chian & E. L. Rempel & C. Rogers, 2007. "Crisis-induced intermittency in non-linear economic cycles," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 211-218.
    11. Chen, Juhn-Horng & Chen, Wei-Ching, 2008. "Chaotic dynamics of the fractionally damped van der Pol equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 188-198.
    12. António M Lopes & J A Tenreiro Machado & John S Huffstot & Maria Eugénia Mata, 2018. "Dynamical analysis of the global business-cycle synchronization," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-25, February.
    13. 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.
    14. 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.
    15. Valls, Claudia, 2012. "Rational integrability of a nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 141-146.
    16. Mulligan, Robert F., 2010. "A fractal comparison of real and Austrian business cycle models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2244-2267.

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