A state-dependent delay equation with chaotic solutions
We exhibit a scalar-valued state-dependent delay differential equation \[ x'(t) = f(x(t - d(x_t))) \] that has a chaotic solution. This equation has continuous (semi-strictly) monotonic negative feedback, and the quantity $t - d(x_t)$ is strictly increasing along solutions.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7246 |
| _version_ | 1797830522841333760 |
|---|---|
| author | Benjamin Kennedy Yiran Mao Erik Wendt |
| author_facet | Benjamin Kennedy Yiran Mao Erik Wendt |
| author_sort | Benjamin Kennedy |
| collection | DOAJ |
| description | We exhibit a scalar-valued state-dependent delay differential equation
\[
x'(t) = f(x(t - d(x_t)))
\]
that has a chaotic solution. This equation has continuous (semi-strictly) monotonic negative feedback, and the quantity $t - d(x_t)$ is strictly increasing along solutions. |
| first_indexed | 2024-04-09T13:37:27Z |
| format | Article |
| id | doaj.art-8f119e1eb5d2479eb92069ecfb48cf08 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:27Z |
| publishDate | 2019-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-8f119e1eb5d2479eb92069ecfb48cf082023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-03-0120192212010.14232/ejqtde.2019.1.227246A state-dependent delay equation with chaotic solutionsBenjamin Kennedy0Yiran Mao1Erik Wendt2Gettysburg College, Gettysburg, PA, U.S.A.Department of Mathematics, Gettysburg College, Gettysburg, PA, U.S.ADepartment of Mathematics, Gettysburg College, Gettysburg, PA, U.S.AWe exhibit a scalar-valued state-dependent delay differential equation \[ x'(t) = f(x(t - d(x_t))) \] that has a chaotic solution. This equation has continuous (semi-strictly) monotonic negative feedback, and the quantity $t - d(x_t)$ is strictly increasing along solutions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7246differential delay equationstate-dependent delaychaotic solution |
| spellingShingle | Benjamin Kennedy Yiran Mao Erik Wendt A state-dependent delay equation with chaotic solutions Electronic Journal of Qualitative Theory of Differential Equations differential delay equation state-dependent delay chaotic solution |
| title | A state-dependent delay equation with chaotic solutions |
| title_full | A state-dependent delay equation with chaotic solutions |
| title_fullStr | A state-dependent delay equation with chaotic solutions |
| title_full_unstemmed | A state-dependent delay equation with chaotic solutions |
| title_short | A state-dependent delay equation with chaotic solutions |
| title_sort | state dependent delay equation with chaotic solutions |
| topic | differential delay equation state-dependent delay chaotic solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7246 |
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