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On the bifurcation of limit cycles in a dynamic model of a small open economy

Published online by Cambridge University Press:  22 February 2013

KATARÍNA MAKOVÍNYIOVÁ  and
RUDOLF ZIMKA
KATARÍNA MAKOVÍNYIOVÁ
Affiliation:
Department of Mathematics and Descriptive Geometry, Technical University in Zvolen, T. G. Masaryka 24, SK-96053 Zvolen, Slovakia email: [email protected]
RUDOLF ZIMKA
Affiliation:
Department of Quantitative Methods and Information Systems, Faculty of Economics, Matej Bel University, Tajovského 10, SK-97590 Banská Bystrica, Slovakia email: [email protected]
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Abstract

In this paper a four-dimensional macroeconomic model of a small open economy, describing the development of income, capital stock, interest rate and money stock, which was constructed in [5] (Makovínyiová, K. & Zimka, R. (2009) On stability in generalized Schinasi's macroeconomic model under fixed exchange rates. Tatra Mt. Math. Publ. 43, 115–122), is analysed. Sufficient conditions for the existence of one pair of purely imaginary eigenvalues and two eigenvalues with negative real parts in the linear approximation matrix of the model are found. Formulae for the calculation of the bifurcation coefficients of the model are derived. A statement about the existence of limit cycles is made. A numerical example is given illustrating the results.

Keywords

Macroeconomic dynamic modelEquilibriumStabilityNormal form of differential equations on centre manifoldBifurcation equationLimit cycle
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 3 , June 2013 , pp. 455 - 470
Copyright
Copyright © Cambridge University Press 2013

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References

[1]Asada, T. (1995) Kaldorian dynamics in an open economy. J. Econ. 62 (3), 239–269.Google Scholar
[2]Bibikov, Yu. N. (1979) Local Theory of Nonlinear Analytic Ordinary Differential Equations, Springer-Verlag, Berlin, Germany.Google Scholar
[3]Kaldor, N. (1940) A model of the trade cycle. Econ. J. 50, 69–86.Google Scholar
[4]Liu, W. M. (1994) Criterion of Hopf bifurcations without using eigenvalues. J. Math. Anal. Appl. 182, 250–256.CrossRefGoogle Scholar
[5]Makovinyiova, K. & Zimka, R. (2009) On stability in generalized Schinasi's macroeconomic model under fixed exchange rates. Tatra Mt. Math. Publ. 43, 115–122.Google Scholar
[6]Minsky, H. P. (1986) Stabilizing an Unstable Economy: A Twentieth Century Fund Report, Yale University Press, 372 pp. ISBN 0-300-03386-9.Google Scholar
[7]Wiggins, S. (2003) Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York.Google Scholar