Stability and Hopf Bifurcation Analysis in a Delayed Myc/E2F/miR-17-92 Network Involving Interlinked Positive and Negative Feedback Loops

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 sta...

Full description

Saved in:
Bibliographic Details
Published inDiscrete dynamics in nature and society Vol. 2018; no. 2018; pp. 1 - 12
Main Authors Wang, Guiyuan, Yang, Zhuoqin
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2018
Hindawi
Hindawi Limited
Wiley
Subjects
Apoptosis
Bifurcation theory
Cell growth
Computer simulation
Delay
Differential equations
Dimensional stability
Economic models
Efficiency
Equilibrium
Feedback loops
Gene expression
Hopf bifurcation
MicroRNAs
Negative feedback
Ordinary differential equations
Physics
Positive feedback
Protein expression
Proteins
Stability analysis
Time lag
Online AccessGet full text

Cover

More Information
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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2018/7014789