A model of regulatory dynamics with threshold-type state-dependent delay
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classical differential equation models with constant or zero time delays is developed to study the stabi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018039 |
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| _version_ | 1832590086813777920 |
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| author | Qingwen Hu |
| author_facet | Qingwen Hu |
| author_sort | Qingwen Hu |
| collection | DOAJ |
| description | We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classical differential equation models with constant or zero time delays is developed to study the stability of steady state, the occurrence and stability of periodic oscillations in regulatory dynamics. Using the method of multiple time scales, we compute the normal form of the general model and show that the state-dependent diffusion time may lead to both supercritical and subcritical Hopf bifurcations. Numerical simulations of the prototype model of Hes1 regulatory dynamics are given to illustrate the general results. |
| format | Article |
| id | doaj-art-e9d95fd50975490c8aa2f6990733f497 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e9d95fd50975490c8aa2f6990733f4972025-01-24T02:40:56ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-07-0115486388210.3934/mbe.2018039A model of regulatory dynamics with threshold-type state-dependent delayQingwen Hu0Department of Mathematical Sciences, The University of Texas at Dallas, 800 W. Campbell Road, FO. 35, Richardson, TX, 75080, USAWe model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classical differential equation models with constant or zero time delays is developed to study the stability of steady state, the occurrence and stability of periodic oscillations in regulatory dynamics. Using the method of multiple time scales, we compute the normal form of the general model and show that the state-dependent diffusion time may lead to both supercritical and subcritical Hopf bifurcations. Numerical simulations of the prototype model of Hes1 regulatory dynamics are given to illustrate the general results.https://www.aimspress.com/article/doi/10.3934/mbe.2018039diffusion timestate-dependent delayhopf bifurcationmultiple time scalesnormal form |
| spellingShingle | Qingwen Hu A model of regulatory dynamics with threshold-type state-dependent delay Mathematical Biosciences and Engineering diffusion time state-dependent delay hopf bifurcation multiple time scales normal form |
| title | A model of regulatory dynamics with threshold-type state-dependent delay |
| title_full | A model of regulatory dynamics with threshold-type state-dependent delay |
| title_fullStr | A model of regulatory dynamics with threshold-type state-dependent delay |
| title_full_unstemmed | A model of regulatory dynamics with threshold-type state-dependent delay |
| title_short | A model of regulatory dynamics with threshold-type state-dependent delay |
| title_sort | model of regulatory dynamics with threshold type state dependent delay |
| topic | diffusion time state-dependent delay hopf bifurcation multiple time scales normal form |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018039 |
| work_keys_str_mv | AT qingwenhu amodelofregulatorydynamicswiththresholdtypestatedependentdelay AT qingwenhu modelofregulatorydynamicswiththresholdtypestatedependentdelay |