The nonlinear GDP dynamics - Ionut Purica (Hyperion Economic Journal, 2013)
The oscillatory behavior of GDP and its components leads to a Fourier transform analysis that results in the eigen values of the dynamic economic system. The larger values are dominating the transient behavior of the GDP components and these transients are discussed along with the specific behavior of each component. The second order differential equations are determined, for each component, to describe the oscillatory behavior and the transient resulting from a step excitation. The natural frequencies are determined and the correlation of pairs of components’ cycles result in ‘beats’ process where the modulated wave cycles are compared and discussed. Based on these correlated influence terms the solutions of the differential equations of each component are determined along with their evolution in the phase space and with the specific Lagrangian. The possible occurrence of dynamical behavior basins for GDP is explored, associated to time interval least action considerations. Important conclusions are drawn from this analysis on the dynamics of GDP and its components, in terms of general versus local equilibriums and their evolution.