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Measuring complexity in a business cycle model of the Kaldor type

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  • Januário, Cristina
  • Grácio, Clara
  • Duarte, Jorge

Abstract

The purpose of this paper is to study the dynamical behavior of a family of two-dimensional nonlinear maps associated to an economic model. Our objective is to measure the complexity of the system using techniques of symbolic dynamics in order to compute the topological entropy. The analysis of the variation of this important topological invariant with the parameters of the system, allows us to distinguish different chaotic scenarios. Finally, we use a another topological invariant to distinguish isentropic dynamics and we exhibit numerical results about maps with the same topological entropy. This work provides an illustration of how our understanding of higher dimensional economic models can be enhanced by the theory of dynamical systems.

Suggested Citation

  • Januário, Cristina & Grácio, Clara & Duarte, Jorge, 2009. "Measuring complexity in a business cycle model of the Kaldor type," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2890-2903.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2890-2903
    DOI: 10.1016/j.chaos.2009.04.030
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    References listed on IDEAS

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    1. Szydłowski, Marek & Krawiec, Adam, 2005. "The stability problem in the Kaldor–Kalecki business cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 299-305.
    2. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2462-2468.
    3. Chu, Peter C., 2006. "First-passage time for stability analysis of the Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1355-1368.
    4. W. W. Chang & D. J. Smyth, 1971. "The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 37-44.
    5. Duarte, Jorge & Silva, Luís & Sousa Ramos, J., 2006. "The influence of coupling on chaotic maps modelling bursting cells," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1314-1326.
    6. El Naschie, M.S., 2006. "Superstrings, entropy and the elementary particles content of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 48-54.
    7. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor–Kalecki model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2405-2413.
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    Cited by:

    1. G. Rigatos & P. Siano & T. Ghosh, 2019. "A Nonlinear Optimal Control Approach to Stabilization of Business Cycles of Finance Agents," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1111-1131, March.
    2. Argentiero, Amedeo & Bovi, Maurizio & Cerqueti, Roy, 2016. "Bayesian estimation and entropy for economic dynamic stochastic models: An exploration of overconsumption," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 143-157.

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