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 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.