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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Main Authors: Yulong Li, Long Zhou, Fengjie Geng
Format: Article
Language:English
Published: AIMS Press 2025-02-01
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.
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publisher AIMS Press
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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