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The inherent complexity in nonlinear business cycle model in resonance

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  • Ma, Junhai
  • Sun, Tao
  • Liu, Lixia

Abstract

Based on Abraham C.-L. Chian’s research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements’ amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:4:p:1104-1112
    DOI: 10.1016/j.chaos.2006.10.013
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    References listed on IDEAS

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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.
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    Cited by:

    1. 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.
    2. 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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