NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL

Wei Li; Xianyi Li

doi:10.11948/2018.1679

2018 Volume 8 Issue 6

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Wei Li, Xianyi Li. NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1679-1693. doi: 10.11948/2018.1679

Citation:

Wei Li, Xianyi Li. NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1679-1693. doi: 10.11948/2018.1679

NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL

Wei Li,
Xianyi Li

Institute of Nonlinear Analysis and Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China

Fund Project:

Abstract

Abstract

In this paper, we derive a semi-discrete system for a nonlinear model of blood cell production. The local stability of its fixed points is investigated by employing a key lemma from[23,24]. It is shown that the system can undergo Neimark-Sacker bifurcation. By using the Center Manifold Theorem, bifurcation theory and normal form method, the conditions for the occurrence of Neimark-Sacker bifurcation and the stability of invariant closed curves bifurcated are also derived. The numerical simulations verify our theoretical analysis and exhibit more complex dynamics of this system.
- Semi-discrete blood cell production model /
- Neimark-Sacker bifurcation /
- invariant closed curve /
- center manifold theorem /
- normal form method
MSC: 39A11;37F45;37G35

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References

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