Stability and Hopf bifurcation analysis in a delayed Myc/E2F/miR-17-92 network involving interlinked positive and negative feedback loops
type: Item
instance of: scholarly article
title: Stability and Hopf bifurcation analysis in a delayed Myc/E2F/miR-17-92 network involving interlinked positive and negative feedback loops
zbMATH Open document ID: 1417.92066
DOI: 10.1155/2018/7014789
author: Guiyuan Wang
author: Zhuoqin Yang
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: MiR-17-92 plays an important role in regulating the levels of the Myc/E2F protein. In this paper, we consider a coupling network between Myc/E2F/miR-17-92 delayed negative feedback loop and Myc/E2F positive feedback loop described by a two-dimensional delay differential equation. Based on linear stability analysis and bifurcation theory, sufficient conditions for stability of equilibria and oscillatory behaviors via Hopf bifurcation are derived when choosing time delay as well as negative feedback strength associated with oscillations as bifurcation parameters, respectively. Furthermore, direction and stability of Hopf bifurcation of time delay are studied by using the normal form method and center manifold theorem. Finally, several numerical simulations are performed to verify the results we obtained.
Mathematics Subject Classification ID: 92C45
Mathematics Subject Classification ID: 92C42
zbMATH DE Number: 7026659
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7014789
OpenAlex ID: W2899782432
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description: scientific article; zbMATH DE number 7026659