Hopf bifurcation and chaos analysis of a discrete-delay dynamic model for a stock market
AbstractThe 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.
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Bibliographic InfoPaper provided by Dipartimento di Scienze Economiche "Marco Fanno" in its series "Marco Fanno" Working Papers with number 0082.
Length: 9 pages
Date of creation: Jul 2008
Date of revision:
dynamic models; bifurcation; Lyapunov exponents; stock market;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-08-06 (All new papers)
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- Dobrescu, Loretti Isabella & Opris, Dumitru, 2007. "Neimark-Sacker bifurcation for the discrete-delay Kaldor model," MPRA Paper 5415, University Library of Munich, Germany.
- Gian-Italo Bischi & Vincenzo Valori, 2000. "Nonlinear effects in a discrete-time dynamic model of a stock market," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2000-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
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