The article proposes a computer program for calculating economic crises according to the generalized mathematical model of S.V. Dubovsky. This model is represented by a system of ordinary nonlinear differential equations with fractional derivatives in the sense of Gerasimov-Caputo with initial conditions. Furthermore, according to a numerical algorithm based on an explicit nonlocal finite-difference scheme, oscillograms and phase trajectories were constructed. It is shown that changing the orders of fractional derivatives in the model can give rise to various modes, for example, damped modes with a steady-state amplitude. It is concluded that the orders of fractional derivatives are responsible for the intensity of the process.

中文翻译：

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在杜博夫斯基广义模型框架内对经济周期进行数值分析的计算机程序

文章根据SV Dubovsky的广义数学模型提出了一种计算经济危机的计算机程序。该模型由具有初始条件的 Gerasimov-Caputo 意义上的分数阶导数的常非线性微分方程系统表示。此外，根据基于显式非局部有限差分格式的数值算法，构建了波形图和相轨迹。结果表明，改变模型中分数阶导数的阶数可以产生各种模式，例如具有稳态幅度的阻尼模式。得出的结论是，分数阶导数的阶数决定了该过程的强度。