title: Ð¡ÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð¼Ð°ÐºÑÐ¾ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Comparative analysis of mathematical models of macroeconomic systems
Creators: name: ÐÐ¸ÑÑÐ¾ÑÐ°Ð½Ð¾Ð², ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: Ð¼Ð¾Ð´ÐµÐ»Ñ
Ð°Ð½Ð°Ð»Ð¸Ð·
Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ
ÑÐ¸ÑÑÐµÐ¼Ð°
ÑÐµÐ¾ÑÐ¸Ñ
Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ
Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ
Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ°
matlab
model
analysis
construction
system
theory
research
description
mathematics

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾ ÑÐ°Ð±Ð¾ÑÑ: Â«Ð¡ÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð¼Ð°ÐºÑÐ¾ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼Â». 1. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼ Ð½Ð° Ð¼Ð°ÐºÑÐ¾ÑÑÐ¾Ð²Ð½Ðµ, Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¾ÑÐ½Ð¾Ð²Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°, Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. 2. Ð Ð¿ÑÐ¾ÑÐµÑÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ» Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½ Ð¾Ð±Ð·Ð¾Ñ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÐºÐ¾-Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¾Ð±Ð·Ð¾ÑÐ° Ð²ÑÐ±ÑÐ°Ð½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð±Ð°Ð»Ð°Ð½ÑÐ°. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¸, ÑÑÐ¾ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¥Ð°ÑÑÐ¾Ð´Ð°-ÐÐ¾Ð¼Ð°ÑÐ° ÑÐ²Ð»ÑÐµÑÑÑ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´ÑÑÐµÐ¹ Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹. 3. Ð Ð¿ÑÐ¾ÑÐµÑÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð° Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ Ð´Ð²Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¾ÑÑÐ°Ð¶Ð°ÑÑÐ¸Ð¹ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¹ Ð¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¹ ÑÐ°ÑÐ°ÐºÑÐµÑ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐµÐ³Ð¾ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð¿ÑÐµÐ´Ð¿ÑÐ¸ÑÑÐ¸Ð¹ Ð½Ð°Ð¹Ð´ÐµÐ½Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ Ð´Ð²ÑÑ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ (Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¸ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹). 4. Ð¢Ð°ÐºÐ¸Ð¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð½ÑÐ¹ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÐºÐ¾Ð½ÐºÑÐµÑÐ½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¿Ð¾ÐºÐ°Ð·Ð°Ð», ÑÑÐ¾ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð°ÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¼Ð°ÐºÑÐ¾ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹. 5. ÐÑÐ¸Ð»Ð¾Ð¶ÐµÐ½Ð¸Ðµ ÑÐ¾Ð´ÐµÑÐ¶Ð¸Ñ ÐºÐ¾Ð´ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² ÑÑÐµÐ´Ðµ MATLAB.
description: The theme of the final qualification work: "Comparative analysis of mathematical models of macroeconomic systems." 1. The algorithms for the study of economic systems at the macro level, using as a basis of mathematical analysis, including mathematical modeling. 2. In the course of the work, a review of existing economic and mathematical models was made. As a result of the review, an economic balance model has been selected. The results of the comparative analysis showed that the modification of the Harrod-Domar model is the most suitable for research. 3. In the course of the research, the selected model was modified and two models were developed, reflecting the linear and non-linear nature. As a result, algorithms for solving these models are proposed. On the basis of the initial data of enterprises, quantitative solutions of two linear models (original and modified) were found. 4. Thus, the comparative analysis of specific results showed that it is necessary to use asymptotic methods for solving macroeconomic models. 5. The application contains the code of the modified model in the MATLAB environment.