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Hopf bifurcation and chaos analysis of a discrete-delay dynamic model for a stock market

Author

Listed:
  • Loretti I. Dobrescu

    (Universita' di Padova)

  • Dumitru Opris

    (West University of Timisoara)

Abstract

The time evolution of prices and saving in a stock market is modelled by a discrete-delay nonlinear dynamical system. The proposed model has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear e¤ects acting out the equilibrium. The analysis of linear approximation through the study of the eigenvalues of the Jacobian matrix is carried out in order to characterize the local stability property and the local bifurcations in the parameter space. If the delay is equal to zero, Lyapunov exponents are calculated. For certain values of the model parameters we prove that the system has a chaotic behaviour. Some numerical examples are finally given for justifying the theoretical results.

Suggested Citation

  • Loretti I. Dobrescu & Dumitru Opris, 2008. "Hopf bifurcation and chaos analysis of a discrete-delay dynamic model for a stock market," "Marco Fanno" Working Papers 0082, Dipartimento di Scienze Economiche "Marco Fanno".
    • Handle: RePEc:pad:wpaper:0082
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    References listed on IDEAS

    as
    1. 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.
    2. Gian-Italo Bischi & Vincenzo Valori, 2000. "Nonlinear effects in a discrete-time dynamic model of a stock market," Working Papers - Mathematical Economics 2000-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
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