The Long Wave in the World Economy: The Present Crisis in Historical Perspective.

Fractional Mathematical Models S.V. Dubovsky to Describe K-Waves in Economics

“…Remark 8. Note that according to dependence (13), with an increase in capital productivity, the accumulation rate decreases. A decrease in the accumulation rate depending on capital productivity means that by increasing the efficiency of using capital productivity, the organization can reduce the amount of its own funds that need to be accumulated to ensure the stable functioning and development of the business.…”

“…where l 1 > 0, l 2 > 0 are coefficients that are determined from statistical data as parameters in the regression equation [57]. However, dependence (13) in his work [14] S.V. Dubovsky did not investigate.…”

“…Remark 5. In article [14], dependence (13) was studied, oscillograms and phase trajectories were obtained for various parameter values, but their economic interpretation was not given.…”

“…Figure 3 shows examples of simply connected regions in which the divergence of the vector field changes its sign: Figure 3a is the accumulation rate function (13), and Figure 3b is the accumulation rate function (14). We will seek a solution to problem (15) using the numerical one-step Adams-Bashforth-Moulton method of the second order of convergence (trapezoidal method).…”

“…We will seek a solution to problem (15) using the numerical one-step Adams-Bashforth-Moulton method of the second order of convergence (trapezoidal method). The phase trajectories obtained according to the numerical method for model (15) are shown in Figure 4 taking into account dependencies (13). Figure 4 shows the calculation of oscillograms and phase trajectories for the dependence ( 13) of the accumulation rate on capital productivity, taking into account different values of l 1 , l 2 and a.…”