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Rational integrability of a nonlinear finance system

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  • Valls, Claudia

Abstract

In this work we study the complexity of the dynamical financial model recently reported in the literaturex˙=z+(y-a)x,y˙=1-by-x2,z˙=-x-cz,by studying its integrability. In particular, we prove that it is not Darbouxian integrable for any value of a, b, c.

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  • Valls, Claudia, 2012. "Rational integrability of a nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 141-146.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:2:p:141-146
    DOI: 10.1016/j.chaos.2011.11.003
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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. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    3. 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.
    4. 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.
    5. Garry J. Schinasi, 1981. "A Nonlinear Dynamic Model of Short Run Fluctuations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 649-656.
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