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Le Sauteur-Robitaille, Justin

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Faculty of Arts and Science - Department of Mathematics and Statistics

André-Aisenstadt Office 5244

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  • MAT1951 A - Introduction aux mathématiques appliquées

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Bifurcation de Hopf dans un modèle de signalement de NF-κB Theses and supervised dissertations / 2018-12
Le Sauteur-Robitaille, Justin
Abstract
The signaling system for the transcription factor NF-?B is involved in over 150 genes in a mammal cell. This leads scientists to try to analyse this molecule to understand its effect on a cell. Many scientists, including Krishna and al., noticed oscillations in the amount of nucleic NF-?B. Before anyone noticed those oscillations, the quantities were thought to be somewhat stable, and they are, but not in every condition. This change of condition creates this instability and the transition of such stability for the stationary solution is caused by a Hopf bifurcation. To determine the existence of the stationary state in the tridimensional system and to analyse the bifurcation is important to predict the oscillations that might appear in certain conditions. It is then necessary to determine what kind of cycle appears or disappears at the bifurcation to understand the stability of those periodic solutions, of those oscillations. Finally, we simulate numercially the bifurcation diagrams for two models and differents parameters to observe the local similarities and global divergence of the diagrams.