Mathematical model of chaos, caused by international trade
DOI:
https://doi.org/10.15587/2312-8372.2013.18208Keywords:
keynesian model, stability problem, phase space, attractor, chaosAbstract
The basic effects and patterns that characterize the Keynesian model of business cycle have been modeled using the system of linear differential equations. The solutions of the system, which describes the interaction of two or three states are found, and stability of this system was investigated. The majority of economic processes proceed in time. Owing to this, corresponding mathematical models are basically dynamic and nonlinear.The similar phenomena were observed in 4 dimentional models for economy of two states. Thus the required combination of parameters has been found, and the hypothesis of chaos as a result of globalization has been proved to be true, even for the elementary models.
References
- Кейнс Дж. Г. Избранные произведения [Текст] / Дж. Г. Кейнс. – М.: Экономика, 1993. – 430 с.
- Линейная модель экономики с "нелинейными" эффектами [Электронный ресурс] // Социнтегрум: цивилизационный форум. – Режим доступа: www/ URL: http://socintegrum.ru/forum/viewtopic.phpt=34&start=0&postdays=0&postorder=asc&highlight=
- Занг, В. Б. Синергетическая экономика. Время и перемены в нелинейной экономической теории [Текст] / В. Б. Занг. – М.: Мир, 1999. – 335 с.
- Малинецкий, Г. Г. Хаос. Структуры. Вычислительный эксперимент. Введение в нелинейную динамику [Текст] / Г. Г. Малинецкий. – М.: Эдиториал УРСС, 2002. – 256 с.
- Федеральная служба государственной статистики [Электронный ресурс]. – Режим доступа: www/ URL: http://www.gks.ru/wps/portal
- Основные статистические данные [Электронный ресурс] // Национальная статистическая служба Республики Армения. – Режим доступа: www/ URL: http://www.armstat.am/ru/
- European Commission [Электронный ресурс]. – Режим доступа: www/ URL: http://epp.eurostat.ec.europa.eu/portal/page_pageid=0,1136217,0_45571467&_dad=portal&_schema=
- Арнольд, В. И. Дополнительные главы теории обыкновенных дифференциальных уравнений [Текст] / В. И. Арнольд. – М.: Наука, 1987. – 304 с.
- Тухвебер, С. М. Модели эволюции многоагентных экономических систем в информационном сообществе (Multi-Agent Economic Systems Evolution Models in Informational Society Preprint, Inst. Appl. Math., the Russian Academy of Science) [Электронный ресурс] / С. М. Тухвебер, В. Г. Редько; ИПМ им. М.В.Келдыша РАН. – Москва, 2005. – Режим доступа: www/ URL: http://www.keldysh.ru/papers/2005/prep22/prep2005_22.html
- Library. The World Factbook [Электронный ресурс] // Central intelligence agency. – Режим доступа: www/ URL: https://www.cia.gov/library/publications/the-world-factbook/geos/am.html
- Keyns, J. G. (1993). Izbrannye proizvedeniya. M.: Ekonomika, 430.
- Lineynaya model' ekonomiki s "nelineynymi" effektami. Sotsintegrum: tsivilizatsionnyy forum. Available: http://socintegrum.ru/forum/viewtopic.php?t=34&start=0&postdays=0&postorder=asc&highlight=
- Zang, V. B. (1999). Sinergeticheskaya ekonomika. Vremya i peremeny v nelineynoy ekonomicheskoy teorii. M.: Mir, 335.
- Malinetskiy, G. G. (2002). Khaos. Struktury. Vychislitel'nyy eksperiment. Vvedenie v nelineynuyu dinamiku. M.: Editorial URSS, 256.
- Federal'naya sluzhba gosudarstvennoy statistiki. Available: http://www.gks.ru/wps/portal
- Osnovnye statisticheskie dannye. Natsional'naya statisticheskaya sluzhba Respubliki Armeniya. Available: http://www.armstat.am/ru/
- European Commission. Available: http://epp.eurostat.ec.europa.eu/portal/page_pageid=0,1136217,0_45571467&_dad=portal&_schema=
- Arnol'd, V. I. (1987). Dopolnitel'nye glavy teorii obyknovennykh differentsial'nykh uravneniy. M.: Nauka, 304.
- Tukhweber, S. M., Red'ko, V. G.; Keldysh Institute of Applied Mathematics (2005). Multi-Agent Economic Systems Evolution Models in Informational Society Preprint, Inst. Appl. Math., the Russian Academy of Science). Moscow. Available: http://www.keldysh.ru/papers/2005/prep22/prep2005_22.html
- Library. The World Factbook. Central intelligence agency. Available: https://www.cia.gov/library/publications/the-world-factbook/geos/am.html
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