Model Solutions for the Motion of a Hypothetical Economy in Ideal Time

1 Model Solutions for the Motion of a Hypothetical Economy in Ideal Time 

The computer assisted experiments reported in this section serve the purpose of numerically substantiating the analytical results presented in Sect. 5.4 and of demonstrating phenomenologically that different combinations of parameters lead to different types of solutions, some representing a motion of the economy approaching a stationary state, and others representing a non-equilibrium motion with periodic limit cycle behaviour. 

In depicting the results use is made of two types of plots, the so called a-plot and b-plot. In terms of a-plots six solutions for (5(r) and x r) are presented as trajectories in the d-x plane in Figs. 5.4a-9a. These figures also contain the functions Fi(d,x) = 0 and F2 d, x) = 0 which are the geometrical loci of the horizontal and vertical fluxlines, the intersections of which represent the singular points P(d, x) for the respective combinations of parameters. Additionally, as b-plots. Figs. 5.4b-9b show the paths of (5(r) and x z) with scaled time r = 2vt for the same parameter combinations. 

Experiment 1. To begin with, a parameter combination is chosen for which the origin d = 0, x = 0 is the only singular point and a stable focus of the motion all trajectories approach the stationary solution 5 = 0, x = 0. Thus the 

Experiment 2. At the threshold value k = 1.5 to the transition to another type of solution, namely that of solutions with sustained cycles, there occurs a critical reduction of the damping effect. Although the origin is still the only singular point and is still - marginally - stable, the oscillatory relaxation takes much more time than in the previous case. 

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