Hopf bifurcation in time‐delayed gene expression model with dimers

Agnieszka Bartłomiejczyk; Marek Bodnar

doi:10.1002/mma.8961

Hopf bifurcation in time‐delayed gene expression model with dimers

Abstract

We study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive steady state and for the existence of the Hopf bifurcation. We check the influence of delay in transcription process on the model dynamics, and we formulate conditions determining the type of the Hopf bifurcation and stability of arising limit cycle.

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Authors (2)

Agnieszka Bartłomiejczyk dr
Marek Bodnar dr hab.
- Uniwersytet Warszawski

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Articles

Type:

artykuły w czasopismach

Published in:

MATHEMATICAL METHODS IN THE APPLIED SCIENCES no. 46, pages 12087 - 12111,
ISSN: 0170-4214

Language:

English

Publication year:

2023

Bibliographic description:

Bartłomiejczyk A., Bodnar M.: Hopf bifurcation in time‐delayed gene expression model with dimers// MATHEMATICAL METHODS IN THE APPLIED SCIENCES -Vol. 46,iss. 11 (2023), s.12087-12111

DOI: