{"title":"1D Piecewise Smooth Map: Exploring a Model of Investment Dynamics under Financial Frictions with Three Types of Investment Projects","authors":"Iryna Sushko, Laura Gardini, Kiminori Matsuyama","doi":"10.1007/s11253-024-02299-7","DOIUrl":null,"url":null,"abstract":"<p>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 [<i>Theor. Econ.</i>, <b>8</b>, 623 (2013); Sec. 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 point of intersection of two curves of this kind is an organizing center, which serves as the origin of infinitely many other bifurcation curves.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02299-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
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 (2013); Sec. 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 point of intersection of two curves of this kind is an organizing center, which serves as the origin of infinitely many other bifurcation curves.
期刊介绍：
Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries.
Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
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