Analytical expressions of periodic disequilibrium fluctuations generated by Hopf bifurcations in economic dynamics

Paper constructs approximate analytical expressions of periodic disequilibrium fluctuations – business cycles – occurring in connection with Hopf bifurcations in economic dynamics. The Kaldorian open economy macrodynamic model with money proposed earlier by the first author is employed as the test m...

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Published inApplied mathematics and computation Vol. 218; no. 13; pp. 7066 - 7077
Main Authors Asada, T., Kalantonis, V., Markakis, M., Markellos, P.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2012
Subjects
Analytical expressions
Bifurcations
Cycles
Dynamic tests
Dynamics
Exact solutions
Fluctuation
Hopf bifurcation
Hopf bifurcations
Macrodynamics
Mathematical analysis
Mathematical models
Stability
Macrodynamics
Cycles
Stability
Analytical expressions
Hopf bifurcations
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Summary:Paper constructs approximate analytical expressions of periodic disequilibrium fluctuations – business cycles – occurring in connection with Hopf bifurcations in economic dynamics. The Kaldorian open economy macrodynamic model with money proposed earlier by the first author is employed as the test model. Its region of equilibrium stability in parameter space is obtained and a Hopf bifurcation curve is identified as a boundary of the region. Validity of the analytical approximations obtained for the cycles generated by the loss of equilibrium stability on this curve is confirmed by comparison to numerically determined cycles. Explicit analytical description of such disequilibrium fluctuations is of particular interest in the case of subcritical bifurcations when the cycles are unstable and their numerical determination is difficult, as in the case of the test model, and may conceivably be useful in testing for subsequent bifurcation of the cycles.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.12.063