Dynamics on semi-discrete Mackey-Glass model
Red blood cells play an extremely important role in human metabolism, and the study of hematopoietic models is of great significance in biology and medicine. A kind of semi-discrete hetmatopoietic model named Mackey-Glass Model was proposed and analyzed in this paper. The existences, stabilities, an...
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025130 |
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| author | Yulong Li Long Zhou Fengjie Geng |
| author_facet | Yulong Li Long Zhou Fengjie Geng |
| author_sort | Yulong Li |
| collection | DOAJ |
| description | Red blood cells play an extremely important role in human metabolism, and the study of hematopoietic models is of great significance in biology and medicine. A kind of semi-discrete hetmatopoietic model named Mackey-Glass Model was proposed and analyzed in this paper. The existences, stabilities, and local dynamics of the fixed points were discussed. By using bifurcation theory, we studied the Neimark-Sacker bifurcation, saddle-node bifurcation, and strong resonance of 1:4. The numerical simulations were presented to illustrate the results of theoretical analysis obtained in this paper, and complex dynamical behaviors were found such as invariant cycles, heteroclinic cycles and Li-Yorke chaos. In addition, a new periodic bubbling phenomenon was discovered in numerical simulations. These not only reflect the richer dynamical behaviors of the semi-discrete models, but also some reflect the complex metabolic characteristics of the hematopoietic system under environmental intervention. |
| format | Article |
| id | doaj-art-5bb81a01fd774a23983128b2816fcc56 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-5bb81a01fd774a23983128b2816fcc562025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011022771280710.3934/math.2025130Dynamics on semi-discrete Mackey-Glass modelYulong Li0Long Zhou1Fengjie Geng2School of Science, China University of Geosciences (Beijing), 100083, Beijing, ChinaSchool of Science, China University of Geosciences (Beijing), 100083, Beijing, ChinaSchool of Science, China University of Geosciences (Beijing), 100083, Beijing, ChinaRed blood cells play an extremely important role in human metabolism, and the study of hematopoietic models is of great significance in biology and medicine. A kind of semi-discrete hetmatopoietic model named Mackey-Glass Model was proposed and analyzed in this paper. The existences, stabilities, and local dynamics of the fixed points were discussed. By using bifurcation theory, we studied the Neimark-Sacker bifurcation, saddle-node bifurcation, and strong resonance of 1:4. The numerical simulations were presented to illustrate the results of theoretical analysis obtained in this paper, and complex dynamical behaviors were found such as invariant cycles, heteroclinic cycles and Li-Yorke chaos. In addition, a new periodic bubbling phenomenon was discovered in numerical simulations. These not only reflect the richer dynamical behaviors of the semi-discrete models, but also some reflect the complex metabolic characteristics of the hematopoietic system under environmental intervention.https://www.aimspress.com/article/doi/10.3934/math.2025130semi-discrete hetmatopoietic modelneimark-sacker bifurcationsaddle-node bifurcationstrong resonance of 1:4numerical simulations |
| spellingShingle | Yulong Li Long Zhou Fengjie Geng Dynamics on semi-discrete Mackey-Glass model AIMS Mathematics semi-discrete hetmatopoietic model neimark-sacker bifurcation saddle-node bifurcation strong resonance of 1:4 numerical simulations |
| title | Dynamics on semi-discrete Mackey-Glass model |
| title_full | Dynamics on semi-discrete Mackey-Glass model |
| title_fullStr | Dynamics on semi-discrete Mackey-Glass model |
| title_full_unstemmed | Dynamics on semi-discrete Mackey-Glass model |
| title_short | Dynamics on semi-discrete Mackey-Glass model |
| title_sort | dynamics on semi discrete mackey glass model |
| topic | semi-discrete hetmatopoietic model neimark-sacker bifurcation saddle-node bifurcation strong resonance of 1:4 numerical simulations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025130 |
| work_keys_str_mv | AT yulongli dynamicsonsemidiscretemackeyglassmodel AT longzhou dynamicsonsemidiscretemackeyglassmodel AT fengjiegeng dynamicsonsemidiscretemackeyglassmodel |