NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL | Zendy

Wei Li | Zendy; Xianyi Li | Zendy

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NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL

Author(s) -

Wei Li,

Xianyi Li

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.1679

Subject(s) - mathematics , center manifold , lemma (botany) , saddle node bifurcation , bifurcation diagram , bifurcation , transcritical bifurcation , mathematical analysis , bifurcation theory , nonlinear system , hopf bifurcation , physics , quantum mechanics , ecology , poaceae , biology

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.

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