Modelling periodic oscillations during somitogenesis
We consider a model of genetic network that has been previously presented by J. Lewis. This model takes the form of delay differential equations with two delays. We give conditions for the local stability of the non-trivial steady state. We investigate the condition underwhich stability is lost and...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.661 |
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| _version_ | 1832590172490825728 |
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| author | Peng Feng Menaka Navaratna |
| author_facet | Peng Feng Menaka Navaratna |
| author_sort | Peng Feng |
| collection | DOAJ |
| description | We consider a model of genetic network that has been previously presented by J. Lewis. This model takes the form of delay differential equations with two delays. We give conditions for the local stability of the non-trivial steady state. We investigate the condition underwhich stability is lost and oscillations occur. In particular, we show that when the ratio of the time delays passes a threshold, sustained oscillations occur through a Hopf bifurcation. Through numerical simulations, we further investigate the ways in which various parameters influence the period and the amplitude of the oscillations. In conclusion, we discuss the implications of our results. |
| format | Article |
| id | doaj-art-249f31d8bb474745b0c777351277501e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-249f31d8bb474745b0c777351277501e2025-01-24T01:54:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-07-014466167310.3934/mbe.2007.4.661Modelling periodic oscillations during somitogenesisPeng Feng0Menaka Navaratna1Department of Physical Sciences and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965Department of Physical Sciences and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965We consider a model of genetic network that has been previously presented by J. Lewis. This model takes the form of delay differential equations with two delays. We give conditions for the local stability of the non-trivial steady state. We investigate the condition underwhich stability is lost and oscillations occur. In particular, we show that when the ratio of the time delays passes a threshold, sustained oscillations occur through a Hopf bifurcation. Through numerical simulations, we further investigate the ways in which various parameters influence the period and the amplitude of the oscillations. In conclusion, we discuss the implications of our results.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.661somitogenesispattern formation.delay differential equations |
| spellingShingle | Peng Feng Menaka Navaratna Modelling periodic oscillations during somitogenesis Mathematical Biosciences and Engineering somitogenesis pattern formation. delay differential equations |
| title | Modelling periodic oscillations during somitogenesis |
| title_full | Modelling periodic oscillations during somitogenesis |
| title_fullStr | Modelling periodic oscillations during somitogenesis |
| title_full_unstemmed | Modelling periodic oscillations during somitogenesis |
| title_short | Modelling periodic oscillations during somitogenesis |
| title_sort | modelling periodic oscillations during somitogenesis |
| topic | somitogenesis pattern formation. delay differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.661 |
| work_keys_str_mv | AT pengfeng modellingperiodicoscillationsduringsomitogenesis AT menakanavaratna modellingperiodicoscillationsduringsomitogenesis |