1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects
UDC 517.9 We consider a 1D continuous piecewise smooth map, which depends on seven parameters. Depending on the values of parameters, it may have up to six branches. This map was proposed by Matsuyama [Theor. Econ., 8, 623–651 (2013); Section 5].  It describes...
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7721 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512705474985984 |
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| author | Sushko, Iryna Gardini, Laura Matsuyama, Kiminori Sushko, Iryna Gardini, Laura Matsuyama, Kiminori |
| author_facet | Sushko, Iryna Gardini, Laura Matsuyama, Kiminori Sushko, Iryna Gardini, Laura Matsuyama, Kiminori |
| author_sort | Sushko, Iryna |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:00Z |
| description | UDC 517.9
We consider a 1D continuous piecewise smooth map, which depends on seven parameters. Depending on the values of parameters, it may have up to six branches. This map was proposed by Matsuyama [Theor. Econ., 8, 623–651 (2013); Section 5].  It describes the macroeconomic dynamics of investment and credit fluctuations in which three types of investment projects compete in the financial market.  We introduce a partitioning of the parameter space according to different branch configurations of the map and illustrate this partitioning for a specific parameter setting.  Then we present an example of the bifurcation structure in a parameter plane, which includes periodicity regions related to superstable cycles. Several bifurcation curves are obtained analytically, in particular, the border-collision bifurcation curves of  fixed points. We show that the intersection point of two  curves of this kind is an organizing center from which infinitely many other bifurcation curves are originated. |
| doi_str_mv | 10.3842/umzh.v75i12.7721 |
| first_indexed | 2026-03-24T03:33:02Z |
| format | Article |
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| id | umjimathkievua-article-7721 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:33:02Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-77212024-06-19T00:35:00Z 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects Sushko, Iryna Gardini, Laura Matsuyama, Kiminori Sushko, Iryna Gardini, Laura Matsuyama, Kiminori 1D piecewise smooth map border-collision bifurcation bifurcation structure investment dynamics under financial frictions UDC 517.9 We consider a 1D continuous piecewise smooth map, which depends on seven parameters. Depending on the values of parameters, it may have up to six branches. This map was proposed by Matsuyama [Theor. Econ., 8, 623–651 (2013); Section 5].  It describes the macroeconomic dynamics of investment and credit fluctuations in which three types of investment projects compete in the financial market.  We introduce a partitioning of the parameter space according to different branch configurations of the map and illustrate this partitioning for a specific parameter setting.  Then we present an example of the bifurcation structure in a parameter plane, which includes periodicity regions related to superstable cycles. Several bifurcation curves are obtained analytically, in particular, the border-collision bifurcation curves of  fixed points. We show that the intersection point of two  curves of this kind is an organizing center from which infinitely many other bifurcation curves are originated. УДК 517.9 Одновимірне кусково-гладке відображення: дослідження моделі інвестиційної динаміки в умовах фінансового тертя з трьоми типами інвестиційних проєктів Розглянуто одновимірне неперервне кусково-гладке відображення, яке залежить від семи параметрів і, в залежності від значень цих параметрів, може мати до шести гілок. Це відображення було запропоновано Мацуямою [Theor. Econ., 8, 623–651 (2013); Section 5] для опису макроекономічної динаміки інвестиційно-кредитних флук\-туацій, в якій три види інвестиційних проєктів конкурують на фінансовому ринку.  Проведено розбиття простору параметрів відповідно до різних  конфігурацій гілок відображення. Це розбиття проілюстровано для конкретного набору параметрів. Крім того, наведено приклад біфуркаційної структури у площині параметрів, що включає області періодичності, пов’язані з надстабільними циклами. Кілька біфуркаційних кривих отримано аналітично, зокрема  біфуркаційні криві зіткнення з межею нерухомих точок.  Показано, що точка перетину двох таких кривих є організуючим центром, що породжує нескінченно багато інших біфуркаційних кривих. Institute of Mathematics, NAS of Ukraine 2024-01-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7721 10.3842/umzh.v75i12.7721 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 12 (2023); 1681 - 1696 Український математичний журнал; Том 75 № 12 (2023); 1681 - 1696 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7721/9934 Copyright (c) 2024 Laura Gardini, Iryna Sushko, Kiminori Matsuyama |
| spellingShingle | Sushko, Iryna Gardini, Laura Matsuyama, Kiminori Sushko, Iryna Gardini, Laura Matsuyama, Kiminori 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title_alt | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title_full | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title_fullStr | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title_full_unstemmed | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title_short | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| title_sort | 1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects |
| topic_facet | 1D piecewise smooth map border-collision bifurcation bifurcation structure investment dynamics under financial frictions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7721 |
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