Critical transitions in a model of a genetic regulatory system
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two methods to numerically test the synthetic time series ge...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.723 |
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| _version_ | 1832590142659887104 |
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| author | Jesse Berwald Marian Gidea |
| author_facet | Jesse Berwald Marian Gidea |
| author_sort | Jesse Berwald |
| collection | DOAJ |
| description | We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two methods to numerically test the synthetic time series generated by the system for early indicators of critical transitions: a detrended fluctuation analysis method, and a novel method based on topological data analysis (persistence diagrams). |
| format | Article |
| id | doaj-art-b61b01ef8fc748ecafd0334c8bd68b73 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b61b01ef8fc748ecafd0334c8bd68b732025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111472374010.3934/mbe.2014.11.723Critical transitions in a model of a genetic regulatory systemJesse Berwald0Marian Gidea1Institute for Mathematics and Its Applications, Minneapolis, MN 55455Yeshiva University, Department of Mathematical Sciences, New York, NY 10016We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two methods to numerically test the synthetic time series generated by the system for early indicators of critical transitions: a detrended fluctuation analysis method, and a novel method based on topological data analysis (persistence diagrams).https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.723critical transitionspersistence diagrams.gene regulatory networksstochastic differential equations |
| spellingShingle | Jesse Berwald Marian Gidea Critical transitions in a model of a genetic regulatory system Mathematical Biosciences and Engineering critical transitions persistence diagrams. gene regulatory networks stochastic differential equations |
| title | Critical transitions in a model of a genetic regulatory system |
| title_full | Critical transitions in a model of a genetic regulatory system |
| title_fullStr | Critical transitions in a model of a genetic regulatory system |
| title_full_unstemmed | Critical transitions in a model of a genetic regulatory system |
| title_short | Critical transitions in a model of a genetic regulatory system |
| title_sort | critical transitions in a model of a genetic regulatory system |
| topic | critical transitions persistence diagrams. gene regulatory networks stochastic differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.723 |
| work_keys_str_mv | AT jesseberwald criticaltransitionsinamodelofageneticregulatorysystem AT mariangidea criticaltransitionsinamodelofageneticregulatorysystem |