Shapovalov中型企业模型的动力学
Dynamics of the Shapovalov mid-size firm model
摘要：
金融和经济过程研究的主要任务之一是预测和分析这些过程的动态。在这项任务中存在重要的研究问题，包括如何确定动态的定性特性，以及如何最好地估计定量指标。这些问题可以从理论和实证两方面进行研究。在经验方法中，人们考虑由时间序列表示的真实数据，识别其动态模式，然后预测过程的短期和长期行为。第二种方法是基于假设的过程中的动力学定律，推导出数学动态模型的基础上，这些法律，并进行后续的分析调查模型所产生的动态。为了实现这些方法，可以使用数值和分析方法。应该注意的是，虽然数值方法可以研究复杂的模型，但由于计算仅在有限的时间间隔内进行，数值误差以及初始数据集的无界空间，使用它们获得可靠结果的可能性受到极大限制。反过来，分析方法使研究人员能够克服这些问题，并获得准确的定性和定量特征的过程动态。然而，它们的有效应用往往局限于低维模型。在本文中，我们开发的分析方法研究确定性动力系统。这些方法不仅可以获得分析稳定性准则和估计极限行为，而且还可以克服与实施定量指标的可靠数值分析有关的困难。我们证明了所提出的方法的有效性，使用中等规模的公司模型建议最近由V.I.沙波瓦洛夫
英文摘要：
One of the main tasks in the study of financial and economic processes is forecasting and analysis of the dynamics of these processes. Within this task lie important research questions including how to determine the qualitative properties of the dynamics and how best to estimate quantitative indicators. These questions can be studied both empirically and theoretically. In the empirical approach, one considers the real data represented by time series, identifies patterns of their dynamics, and then forecasts short- and long-term behavior of the process. The second approach is based on postulating the laws of dynamics for the process, deriving mathematical dynamic models based on these laws, and conducting subsequent analytical investigation of the dynamics generated by the models. To implement these approaches, both numerical and analytical methods can be used. It should be noted that while numerical methods make it possible to study complex models, the possibility of obtaining reliable results using them is significantly limited due to calculations being performed only over finite-time intervals, numerical errors, and the unbounded space of initial data sets. In turn, analytical methods allow researchers to overcome these problems and to obtain exact qualitative and quantitative characteristics of the process dynamics. However, their effective applications are often limited to low-dimensional models. In this paper, we develop analytical methods for the study of deterministic dynamic systems. These methods make it possible not only to obtain analytical stability criteria and to estimate limiting behavior, but also to overcome the difficulties related to implementing reliable numerical analysis of quantitative indicators. We demonstrate the effectiveness of the proposed methods using the mid-size firm model suggested recently by V.I. Shapovalov.
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