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.
翻译:文章根据S.V. Dubovsky的通用数学模型,提出了一个计算经济危机的计算机程序。该模型代表着一种普通的非线性差分方程式,其分数衍生物在Gerasimov-Caputo的意义上具有初始条件。此外,根据基于明确的非本地有限差异计划的数字算法,还构建了秒形图和相向轨迹。这表明改变模型中分数衍生物的顺序可产生多种模式,例如,稳定状态振荡的摇动模式。得出的结论是,分数衍生物的顺序对过程的强度负有责任。