@article{Li2025, 
author = {Yulong Li and Long Zhou and Fengjie Geng},
title = {Dynamics on semi-discrete Mackey-Glass model},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {2771-2807},
keywords = {semi-discrete hetmatopoietic model, Neimark-Sacker bifurcation, saddle-node bifurcation, strong resonance of 1:4, numerical simulations},
url = {https://www.sciopen.com/article/10.3934/math.2025130},
doi = {10.3934/math.2025130},
abstract = {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.}
}