Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition
UDC 517.9 Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition is studied by using a nonstandard finite-difference scheme.  We prove that a series of numerical Neimark–Sacker bifurcations appear at the positive equilibrium as th...
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| author | Liu, Xueyang Wang, Qi Liu, Xueyang Wang, Qi |
| author_facet | Liu, Xueyang Wang, Qi Liu, Xueyang Wang, Qi |
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Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition is studied by using a nonstandard finite-difference scheme.  We prove that a series of numerical Neimark–Sacker bifurcations appear at the positive equilibrium as the time delay increases. At the same time, the parameter conditions for the existence of numerical Neimark–Sacker bifurcations at positive equilibrium point are presented. Finally, we use several examples to verify the accuracy of the results. |
| doi_str_mv | 10.3842/umzh.v76i1.7295 |
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Ukrainian Mathematical Journal
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Numerical Bifurcation of a Delayed Diffusive Hematopoiesis Model with Dirichlet Boundary Conditions
Published: 30 July 2024
Volume 76, pages 157–167, (2024)
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Xueyang Liu1 &
Qi Wang1
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Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition is studied by using a nonstandard finite-difference scheme. We prove that a series of numerical Neimark– Sacker bifurcations appears at the positive equilibrium as the time delay increases. At the same time, the parameter conditions for the existence of numerical Neimark–Sacker bifurcations at the point of positive equilibrium are presented. Finally, we present several examples to verify the accuracy of the accumulated results.
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School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, China
Xueyang Liu & Qi Wang
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 1, pp. 147–156, January, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i1.7295.
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Liu, X., Wang, Q. Numerical Bifurcation of a Delayed Diffusive Hematopoiesis Model with Dirichlet Boundary Conditions.
Ukr Math J 76, 157–167 (2024). https://doi.org/10.1007/s11253-024-02314-x
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Received: 21 August 2022
Published: 30 July 2024
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DOI: https://doi.org/10.1007/s11253-024-02314-x
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| id | umjimathkievua-article-7295 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:14Z |
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| publisher | Institute of Mathematics, NAS of Ukraine |
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| spelling | umjimathkievua-article-72952024-06-19T00:35:02Z Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition Liu, Xueyang Wang, Qi Liu, Xueyang Wang, Qi hematopoiesis model nonstandard finite difference scheme bifurcation computional mathematics UDC 517.9 Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition is studied by using a nonstandard finite-difference scheme.  We prove that a series of numerical Neimark–Sacker bifurcations appear at the positive equilibrium as the time delay increases. At the same time, the parameter conditions for the existence of numerical Neimark–Sacker bifurcations at positive equilibrium point are presented. Finally, we use several examples to verify the accuracy of the results. УДК 517.9 Чисельна біфуркація моделі сповільненого дифузного кровотворення з граничною умовою Діріхле  За допомогою нестандартної скінченно-різницевої схеми досліджено числову біфуркацію в моделі сповільненого дифузійного кровотворення з граничною умовою Діріхле. Доведено, що при збільшенні часу запізнення в точці позитивної рівноваги з'являється серія числових біфуркацій Неймарка–Сакера. Крім того, наведено параметричні умови існування числових біфуркацій Неймарка–Сакера в точці позитивної рівноваги. Насамкінець наведено кілька прикладів для перевірки точності отриманих результатів.  Institute of Mathematics, NAS of Ukraine 2024-02-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7295 10.3842/umzh.v76i1.7295 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 1 (2024); 147 - 156 Український математичний журнал; Том 76 № 1 (2024); 147 - 156 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7295/9685 Copyright (c) 2024 Qi Wang, Xueyang Liu |
| spellingShingle | Liu, Xueyang Wang, Qi Liu, Xueyang Wang, Qi Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title | Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title_alt | Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title_full | Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title_fullStr | Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title_full_unstemmed | Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title_short | Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition |
| title_sort | numerical bifurcation of a delayed diffusive hematopoiesis model with dirichlet boundary condition |
| topic_facet | hematopoiesis model nonstandard finite difference scheme bifurcation computional mathematics |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7295 |
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